christopher/oeis · Datasets at Hugging Face

sequence_id stringlengths 7 7	sequence_name stringlengths 4 573	sequence listlengths 1 348	keywords listlengths 1 8	score int64 1 2.35k	offset_a int64 -14,827 666,262,453B	offset_b int64 0 635M ⌀	cross_references listlengths 1 128 ⌀	former_ids listlengths 1 3 ⌀	author stringlengths 7 231 ⌀	timestamp timestamp[us]date 1999-12-11 03:00:00 2025-07-19 00:40:46	filename stringlengths 29 29	hash stringlengths 32 32
A011901	a(n) = floor( n(n-1)(n-2)/19 ).	[ "0", "0", "0", "0", "1", "3", "6", "11", "17", "26", "37", "52", "69", "90", "114", "143", "176", "214", "257", "306", "360", "420", "486", "559", "639", "726", "821", "923", "1034", "1153", "1282", "1419", "1566", "1722", "1889", "2066", "2254", "2453", "2664", "2886", "3120", "3366", "3625", "3897", "4182", "4481", "4793", "5120", "5461", "5818", "6189", "6576", "6978", "7397", "7832", "8284", "8753", "9240", "9744", "10266", "10806", "11365", "11943", "12540", "13157", "13793", "14450", "15127" ]	[ "nonn", "easy" ]	33	0	6	[ "A011886", "A011901" ]	null	N. J. A. Sloane	2025-02-01T19:54:37	oeisdata/seq/A011/A011901.seq	a9cc74f34c9355795c9a5f36f3c9c170
A011902	a(n) = floor( n(n-1)(n-2)/20 ).	[ "0", "0", "0", "0", "1", "3", "6", "10", "16", "25", "36", "49", "66", "85", "109", "136", "168", "204", "244", "290", "342", "399", "462", "531", "607", "690", "780", "877", "982", "1096", "1218", "1348", "1488", "1636", "1795", "1963", "2142", "2331", "2530", "2741", "2964", "3198", "3444", "3702", "3973", "4257", "4554", "4864", "5188", "5527", "5880", "6247", "6630", "7027", "7441", "7870", "8316", "8778", "9256", "9752", "10266", "10797", "11346", "11913", "12499", "13104", "13728", "14371" ]	[ "nonn", "easy" ]	22	0	6	[ "A011886", "A011902" ]	null	N. J. A. Sloane	2024-10-18T06:08:35	oeisdata/seq/A011/A011902.seq	3db55d2640963b5240c58ce76c81370a
A011903	a(n) = floor(n(n-1)(n-2)/21).	[ "0", "0", "0", "0", "1", "2", "5", "10", "16", "24", "34", "47", "62", "81", "104", "130", "160", "194", "233", "276", "325", "380", "440", "506", "578", "657", "742", "835", "936", "1044", "1160", "1284", "1417", "1558", "1709", "1870", "2040", "2220", "2410", "2611", "2822", "3045", "3280" ]	[ "nonn", "easy" ]	27	0	6	[ "A011886", "A011903" ]	null	N. J. A. Sloane	2024-10-18T01:19:47	oeisdata/seq/A011/A011903.seq	2c1159a6ed72b0d42ac955ac0693cc56
A011904	a(n) = floor( n(n-1)(n-2)/22 ).	[ "0", "0", "0", "0", "1", "2", "5", "9", "15", "22", "32", "45", "60", "78", "99", "124", "152", "185", "222", "264", "310", "362", "420", "483", "552", "627", "709", "797", "893", "996", "1107", "1225", "1352", "1488", "1632", "1785", "1947", "2119", "2300", "2492", "2694", "2907", "3130", "3365", "3612", "3870", "4140", "4422", "4717", "5024", "5345", "5679", "6027", "6388", "6764", "7155", "7560", "7980", "8415", "8866", "9332", "9815", "10314", "10830", "11362", "11912", "12480", "13065", "13668" ]	[ "nonn", "easy" ]	24	0	6	[ "A011886", "A011904" ]	null	N. J. A. Sloane	2024-10-18T06:08:35	oeisdata/seq/A011/A011904.seq	ee74c93d8ad679aa5fdc3e4a7de7e408
A011905	a(n) = floor( n(n-1)(n-2)/23 ).	[ "0", "0", "0", "0", "1", "2", "5", "9", "14", "21", "31", "43", "57", "74", "94", "118", "146", "177", "212", "252", "297", "346", "401", "462", "528", "600", "678", "763", "854", "953", "1059", "1172", "1293", "1423", "1561", "1707", "1862", "2026", "2200", "2384", "2577", "2780", "2994", "3219", "3454", "3701", "3960", "4230", "4512", "4806", "5113", "5432", "5765", "6111", "6470", "6843", "7231", "7633", "8049", "8480", "8926", "9388", "9866", "10359", "10868", "11394", "11937", "12496", "13073" ]	[ "nonn", "easy" ]	22	0	6	[ "A011886", "A011905" ]	null	N. J. A. Sloane	2024-10-18T06:08:35	oeisdata/seq/A011/A011905.seq	7a9c2e2b1c810085307ca3749d90187b
A011906	If b(n) is A011900(n) and c(n) is A001109(n), then a(n) = b(n)*c(n) = b(n) + (b(n)+1) + (b(n)+2) + ... + c(n).	[ "1", "18", "525", "17340", "586177", "19896030", "675781821", "22956120408", "779829016225", "26491211221770", "899921240562957", "30570830315362260", "1038508305678375841", "35278711540581704598", "1198437683944896688125", "40711602541832856049200", "1382996048733983114022337" ]	[ "nonn", "easy" ]	30	1	2	[ "A001109", "A011900", "A011906", "A029547", "A091761" ]	null	Mario Velucchi (mathchess(AT)velucchi.it)	2024-10-18T06:08:52	oeisdata/seq/A011/A011906.seq	9b98ee8837ea3ff90f5e9994ce8e91bd
A011907	a(n) = floor( n(n-1)(n-2)/25 ).	[ "0", "0", "0", "0", "0", "2", "4", "8", "13", "20", "28", "39", "52", "68", "87", "109", "134", "163", "195", "232", "273", "319", "369", "425", "485", "552", "624", "702", "786", "876", "974", "1078", "1190", "1309", "1436", "1570", "1713", "1864", "2024", "2193", "2371", "2558", "2755", "2961", "3178", "3405", "3643", "3891", "4151", "4421", "4704", "4998", "5304", "5622", "5952", "6296", "6652", "7022", "7405", "7802", "8212", "8637", "9076", "9530", "9999", "10483", "10982", "11497", "12027" ]	[ "nonn", "easy" ]	18	0	6	[ "A011886", "A011907" ]	null	N. J. A. Sloane	2024-10-18T06:09:22	oeisdata/seq/A011/A011907.seq	b3f902d52eeca675231803d87b655abc
A011908	a(n) = floor( n(n-1)(n-2)/26 ).	[ "0", "0", "0", "0", "0", "2", "4", "8", "12", "19", "27", "38", "50", "66", "84", "105", "129", "156", "188", "223", "263", "306", "355", "408", "467", "530", "600", "675", "756", "843", "936", "1037", "1144", "1259", "1380", "1510", "1647", "1793", "1946", "2109", "2280", "2460", "2649", "2847", "3056", "3274", "3503", "3741", "3991", "4251", "4523", "4805", "5100", "5406", "5724", "6054", "6396", "6752", "7120" ]	[ "nonn" ]	19	0	6	[ "A011886", "A011908" ]	null	N. J. A. Sloane	2024-10-18T06:29:57	oeisdata/seq/A011/A011908.seq	b87a102d9573125606119b51ed1ab205
A011909	a(n) = floor( n(n-1)(n-2)/27 ).	[ "0", "0", "0", "0", "0", "2", "4", "7", "12", "18", "26", "36", "48", "63", "80", "101", "124", "151", "181", "215", "253", "295", "342", "393", "449", "511", "577", "650", "728", "812", "902", "998", "1102", "1212", "1329", "1454", "1586", "1726", "1874", "2030", "2195", "2368", "2551", "2742", "2943", "3153", "3373", "3603", "3843", "4094", "4355", "4627", "4911", "5205", "5512", "5830", "6160", "6502", "6856", "7224", "7604", "7997", "8404", "8824", "9258", "9706", "10168", "10645", "11136" ]	[ "nonn" ]	24	0	6	[ "A011886", "A011909" ]	null	N. J. A. Sloane	2024-10-19T21:27:32	oeisdata/seq/A011/A011909.seq	48229318a86f5ee9ff7000043abfea1b
A011910	a(n) = floor( n(n-1)(n-2)/28 ).	[ "0", "0", "0", "0", "0", "2", "4", "7", "12", "18", "25", "35", "47", "61", "78", "97", "120", "145", "174", "207", "244", "285", "330", "379", "433", "492", "557", "626", "702", "783", "870", "963", "1062", "1169", "1282", "1402", "1530", "1665", "1807", "1958", "2117", "2284", "2460", "2644", "2838", "3040", "3252", "3474", "3706", "3948", "4200", "4462", "4735", "5019", "5315", "5621", "5940", "6270", "6612", "6966", "7332", "7712", "8104", "8509", "8928", "9360", "9805", "10265", "10739", "11227" ]	[ "nonn", "easy" ]	28	0	6	[ "A011886", "A011910" ]	null	N. J. A. Sloane	2024-10-19T21:27:48	oeisdata/seq/A011/A011910.seq	a1b8b21b8326e85c5bd040890d982b0d
A011911	a(n) = floor( n(n-1)(n-2)/29 ).	[ "0", "0", "0", "0", "0", "2", "4", "7", "11", "17", "24", "34", "45", "59", "75", "94", "115", "140", "168", "200", "235", "275", "318", "366", "418", "475", "537", "605", "677", "756", "840", "930", "1026", "1128", "1238", "1354", "1477", "1607", "1745", "1890", "2044", "2205", "2375", "2553", "2740", "2935", "3140", "3354", "3578", "3811", "4055", "4308", "4572", "4846", "5131", "5427", "5735", "6053", "6384", "6726", "7080", "7446", "7824", "8216", "8620", "9037", "9467", "9911", "10368", "10840" ]	[ "nonn" ]	19	0	6	[ "A011886", "A011911" ]	null	N. J. A. Sloane	2025-01-25T12:50:35	oeisdata/seq/A011/A011911.seq	f28f61dbe1d461e00b6286e349e3789e
A011912	a(n) = floor(n(n-1)(n-2)/30).	[ "0", "0", "0", "0", "0", "2", "4", "7", "11", "16", "24", "33", "44", "57", "72", "91", "112", "136", "163", "193", "228", "266", "308", "354", "404", "460", "520", "585", "655", "730", "812", "899", "992", "1091", "1196", "1309", "1428", "1554", "1687", "1827", "1976", "2132", "2296", "2468", "2648", "2838", "3036", "3243", "3459", "3684", "3920", "4165", "4420", "4685", "4960", "5247", "5544", "5852", "6171", "6501", "6844", "7198", "7564", "7942", "8332", "8736", "9152", "9581", "10023", "10478", "10948" ]	[ "nonn", "easy" ]	34	0	6	[ "A011886", "A011912" ]	null	N. J. A. Sloane	2024-10-19T21:36:49	oeisdata/seq/A011/A011912.seq	713542d8068c39cf534e0368b7d32f9a
A011913	a(n) = floor(n(n - 1)(n - 2)/31).	[ "0", "0", "0", "0", "0", "1", "3", "6", "10", "16", "23", "31", "42", "55", "70", "88", "108", "131", "157", "187", "220", "257", "298", "342", "391", "445", "503", "566", "634", "707", "785", "870", "960", "1056", "1158", "1266", "1381", "1503", "1632", "1768", "1912", "2063", "2221", "2388", "2563", "2746", "2938", "3138", "3347", "3565", "3793", "4030", "4277", "4534", "4800", "5077", "5365", "5663", "5972", "6292", "6623", "6965", "7320", "7686", "8064", "8454", "8856", "9271", "9699", "10140", "10594" ]	[ "nonn" ]	22	0	7	[ "A011886", "A011913" ]	null	N. J. A. Sloane	2024-10-19T21:40:03	oeisdata/seq/A011/A011913.seq	237cfbc41bab4f73dde7d1b0ec629eff
A011914	a(n) = floor(n(n - 1)(n - 2)/32).	[ "0", "0", "0", "0", "0", "1", "3", "6", "10", "15", "22", "30", "41", "53", "68", "85", "105", "127", "153", "181", "213", "249", "288", "332", "379", "431", "487", "548", "614", "685", "761", "842", "930", "1023", "1122", "1227", "1338", "1456", "1581", "1713", "1852", "1998", "2152", "2313", "2483", "2660", "2846", "3040", "3243", "3454", "3675", "3904", "4143", "4392", "4650", "4919", "5197", "5486", "5785", "6095", "6416", "6748", "7091", "7445", "7812", "8190" ]	[ "nonn", "easy" ]	26	0	7	[ "A011886", "A011914" ]	null	N. J. A. Sloane, Dec 11 1996	2024-10-21T04:34:36	oeisdata/seq/A011/A011914.seq	820c7097ee2f64246c52a345201777d9
A011915	a(n) = floor(n(n-1)(n-2)*(n-3)/5).	[ "0", "0", "0", "0", "4", "24", "72", "168", "336", "604", "1008", "1584", "2376", "3432", "4804", "6552", "8736", "11424", "14688", "18604", "23256", "28728", "35112", "42504", "51004", "60720", "71760", "84240", "98280", "114004", "131544", "151032", "172608", "196416", "222604", "251328", "282744", "317016", "354312" ]	[ "nonn", "easy" ]	32	0	5	[ "A000332", "A011795", "A011915", "A011917", "A011919", "A011921", "A011923", "A011924", "A011925", "A011926", "A011927", "A011928", "A011929", "A011930", "A011931", "A011932", "A011933", "A011935", "A011936", "A011937", "A011938", "A011939", "A011940", "A011941", "A011942", "A033486", "A033487", "A033488", "A034827", "A050534", "A052762", "A162668" ]	null	N. J. A. Sloane	2024-12-30T04:00:15	oeisdata/seq/A011/A011915.seq	9b4376dd6434a98133e1a50ce73ee115
A011916	a(n) = ((b(n)-1)+sqrt(3b(n)^2-4b(n)+1))/2, where b(n) is A011922(n).	[ "0", "3", "44", "615", "8568", "119339", "1662180", "23151183", "322454384", "4491210195", "62554488348", "871271626679", "12135248285160", "169022204365563", "2354175612832724", "32789436375292575", "456697933641263328", "6360981634602394019" ]	[ "nonn", "easy" ]	47	0	2	[ "A011916", "A011918", "A109437" ]	null	Mario Velucchi (mathchess(AT)velucchi.it)	2018-07-26T18:41:16	oeisdata/seq/A011/A011916.seq	868a6c5ba3304877791022510915654d
A011917	[ n(n-1)(n-2)(n-3)/7 ].	[ "0", "0", "0", "0", "3", "17", "51", "120", "240", "432", "720", "1131", "1697", "2451", "3432", "4680", "6240", "8160", "10491", "13289", "16611", "20520", "25080", "30360", "36432", "43371", "51257", "60171", "70200", "81432", "93960", "107880", "123291", "140297", "159003" ]	[ "nonn", "easy", "changed" ]	15	0	5	null	null	N. J. A. Sloane	2025-07-08T02:42:25	oeisdata/seq/A011/A011917.seq	93707e190097b03d695d055c532eebb0
A011918	a(n) = A011916(n) + A011922(n) - 1.	[ "5", "76", "1065", "14840", "206701", "2878980", "40099025", "558507376", "7779004245", "108347552060", "1509086724601", "21018866592360", "292755045568445", "4077551771365876", "56792969753553825", "791024024778387680", "11017543377143873701", "153454583255235844140", "2137346622196157944265" ]	[ "nonn", "easy" ]	28	1	1	[ "A011916", "A011918" ]	null	Mario Velucchi (mathchess(AT)velucchi.it)	2016-03-05T05:25:14	oeisdata/seq/A011/A011918.seq	8fcaa223669cc5af067a6eaa83d49f06
A011919	a(n) = floor(n(n-1)(n-2)*(n-3)/9).	[ "0", "0", "0", "0", "2", "13", "40", "93", "186", "336", "560", "880", "1320", "1906", "2669", "3640", "4853", "6346", "8160", "10336", "12920", "15960", "19506", "23613", "28336", "33733", "39866", "46800", "54600", "63336", "73080", "83906", "95893", "109120", "123669", "139626", "157080", "176120", "196840", "219336", "243706", "270053", "298480" ]	[ "nonn", "easy" ]	15	0	5	null	null	N. J. A. Sloane	2022-10-18T15:28:39	oeisdata/seq/A011/A011919.seq	9df3ece1c12d693902300b81a737c61f
A011920	a(n) = b(n)*(b(n)+1) = b(n) + ... + c(n), where b(n) = A011916(n), c(n) = A011918(n).	[ "12", "1980", "378840", "73419192", "14241916260", "2762844014580", "535977297450672", "103976830083273840", "20170969020163148220", "3913064012542622257452", "759114247456742016195720", "147264250942490855924510760" ]	[ "nonn", "easy" ]	19	1	1	null	null	Mario Velucchi (mathchess(AT)velucchi.it)	2024-02-07T11:55:29	oeisdata/seq/A011/A011920.seq	3f693d92f833a3d724992930c6a9c54e
A011921	[ n(n-1)(n-2)(n-3)/11 ].	[ "0", "0", "0", "0", "2", "10", "32", "76", "152", "274", "458", "720", "1080", "1560", "2184", "2978", "3970", "5192", "6676", "8456", "10570", "13058", "15960", "19320", "23184", "27600", "32618", "38290", "44672", "51820", "59792", "68650", "78458", "89280", "101184" ]	[ "nonn", "easy", "changed" ]	15	0	5	null	null	N. J. A. Sloane	2025-07-08T02:42:31	oeisdata/seq/A011/A011921.seq	22916ed228542b90969fcc5bed50448c
A011922	a(n) = 15a(n-1) - 15a(n-2) + a(n-3) with a(0)=1, a(1)=3, and a(2)=33.	[ "1", "3", "33", "451", "6273", "87363", "1216801", "16947843", "236052993", "3287794051", "45793063713", "637815097923", "8883618307201", "123732841202883", "1723376158533153", "24003533378261251", "334326091137124353", "4656561742541479683", "64857538304443591201", "903348974519668797123", "12582028104970919568513" ]	[ "nonn", "easy", "changed" ]	90	0	2	[ "A001075", "A001353", "A007655", "A011916", "A011918", "A011920", "A011922", "A011943", "A103974" ]	null	Mario Velucchi (mathchess(AT)velucchi.it)	2025-07-10T04:32:18	oeisdata/seq/A011/A011922.seq	82a375d07870a63c0fc993881bf3a42c
A011923	[ n(n-1)(n-2)(n-3)/13 ].	[ "0", "0", "0", "0", "1", "9", "27", "64", "129", "232", "387", "609", "913", "1320", "1848", "2520", "3360", "4393", "5649", "7155", "8944", "11049", "13504", "16347", "19617", "23353", "27600", "32400", "37800", "43848", "50593", "58089", "66387", "75544", "85617", "96664" ]	[ "nonn", "easy", "changed" ]	16	0	6	null	null	N. J. A. Sloane	2025-07-08T02:42:36	oeisdata/seq/A011/A011923.seq	f4c79dac57d8f07786d55e8c5f08027d
A011924	Floor[n(n-1)(n-2)(n-3)/14].	[ "0", "0", "0", "0", "1", "8", "25", "60", "120", "216", "360", "565", "848", "1225", "1716", "2340", "3120", "4080", "5245", "6644", "8305", "10260", "12540", "15180", "18216", "21685", "25628", "30085", "35100", "40716", "46980", "53940", "61645", "70148", "79501", "89760" ]	[ "nonn", "easy", "changed" ]	28	0	6	null	null	N. J. A. Sloane	2025-07-08T02:42:43	oeisdata/seq/A011/A011924.seq	3f0d0619f86940a49d364bf44820838b
A011925	a(n) = floor(n(n-1)(n-2)*(n-3)/15).	[ "0", "0", "0", "0", "1", "8", "24", "56", "112", "201", "336", "528", "792", "1144", "1601", "2184", "2912", "3808", "4896", "6201", "7752", "9576", "11704", "14168", "17001", "20240", "23920", "28080", "32760", "38001", "43848", "50344", "57536", "65472", "74201", "83776" ]	[ "nonn", "easy" ]	28	0	6	null	null	N. J. A. Sloane	2022-09-08T08:44:37	oeisdata/seq/A011/A011925.seq	156b845c98c772931fae65e698121902
A011926	a(n) = floor(n(n-1)(n-2)*(n-3)/16).	[ "0", "0", "0", "0", "1", "7", "22", "52", "105", "189", "315", "495", "742", "1072", "1501", "2047", "2730", "3570", "4590", "5814", "7267", "8977", "10972", "13282", "15939", "18975", "22425", "26325", "30712", "35626", "41107", "47197", "53940", "61380", "69564", "78540" ]	[ "nonn", "easy", "changed" ]	22	0	6	null	null	N. J. A. Sloane	2025-07-08T02:42:48	oeisdata/seq/A011/A011926.seq	75700869a54159d746f24585f6d1f057
A011927	[ n(n-1)(n-2)(n-3)/17 ].	[ "0", "0", "0", "0", "1", "7", "21", "49", "98", "177", "296", "465", "698", "1009", "1413", "1927", "2569", "3360", "4320", "5472", "6840", "8449", "10327", "12501", "15001", "17858", "21105", "24776", "28905", "33530", "38689", "44421", "50767", "57769", "65472", "73920" ]	[ "nonn", "easy", "changed" ]	15	0	6	null	null	N. J. A. Sloane	2025-07-08T02:42:58	oeisdata/seq/A011/A011927.seq	22a878d18ed2a30c829a8846dd79c5a9
A011928	a(n) = floor(n(n-1)(n-2)(n-3)/18).	[ "0", "0", "0", "0", "1", "6", "20", "46", "93", "168", "280", "440", "660", "953", "1334", "1820", "2426", "3173", "4080", "5168", "6460", "7980", "9753", "11806", "14168", "16866", "19933", "23400", "27300", "31668", "36540", "41953", "47946", "54560", "61834", "69813", "78540", "88060", "98420", "109668", "121853", "135026", "149240" ]	[ "nonn", "easy" ]	16	0	6	null	null	N. J. A. Sloane	2022-10-18T15:28:21	oeisdata/seq/A011/A011928.seq	29f673e697e4c573654c817f59a3b75b
A011929	a(n) = floor(n(n-1)(n-2)(n-3)/19).	[ "0", "0", "0", "0", "1", "6", "18", "44", "88", "159", "265", "416", "625", "903", "1264", "1724", "2298", "3006", "3865", "4896", "6120", "7560", "9240", "11185", "13422", "15978", "18884", "22168", "25863", "30001", "34616", "39745", "45423", "51688", "58580", "66138", "74406", "83425", "93240", "103896", "115440", "127920", "141385" ]	[ "nonn", "easy" ]	16	0	6	null	null	N. J. A. Sloane	2022-10-18T15:29:00	oeisdata/seq/A011/A011929.seq	1ab9c5069c36ceeca5d3be524c60cad7
A011930	a(n) = floor(n(n-1)(n-2)(n-3)/20).	[ "0", "0", "0", "0", "1", "6", "18", "42", "84", "151", "252", "396", "594", "858", "1201", "1638", "2184", "2856", "3672", "4651", "5814", "7182", "8778", "10626", "12751", "15180", "17940", "21060", "24570", "28501", "32886", "37758", "43152", "49104", "55651", "62832", "70686", "79254", "88578", "98701" ]	[ "nonn", "easy" ]	28	0	6	null	null	N. J. A. Sloane	2023-06-13T09:04:50	oeisdata/seq/A011/A011930.seq	8225bdbf5477cff08d3a8925a7a97f5b
A011931	a(n) = floor(n(n-1)(n-2)*(n-3)/21).	[ "0", "0", "0", "0", "1", "5", "17", "40", "80", "144", "240", "377", "565", "817", "1144", "1560", "2080", "2720", "3497", "4429", "5537", "6840", "8360", "10120", "12144", "14457", "17085", "20057", "23400", "27144", "31320", "35960", "41097", "46765", "53001", "59840", "67320", "75480", "84360", "94001", "104445", "115737", "127920", "141040", "155144", "170280", "186497", "203845", "222377", "242144" ]	[ "nonn", "easy", "changed" ]	19	0	6	null	null	N. J. A. Sloane	2025-07-07T18:49:18	oeisdata/seq/A011/A011931.seq	102c53d0a40f130f2c1105471886c3f6
A011932	a(n) = floor( n(n-1)(n-2)*(n-3)/22 ).	[ "0", "0", "0", "0", "1", "5", "16", "38", "76", "137", "229", "360", "540", "780", "1092", "1489", "1985", "2596", "3338", "4228", "5285", "6529", "7980", "9660", "11592", "13800", "16309", "19145", "22336", "25910", "29896", "34325", "39229", "44640", "50592", "57120", "64260", "72049", "80525", "89728", "99698", "110476", "122105", "134629", "148092", "162540", "178020", "194580", "212269", "231137" ]	[ "nonn", "easy" ]	19	0	6	[ "A011915", "A011932" ]	null	N. J. A. Sloane	2024-11-03T09:33:48	oeisdata/seq/A011/A011932.seq	22e93c230e099e43fbf25525d70d8839
A011933	a(n) = floor( n(n-1)(n-2)*(n-3)/23 ).	[ "0", "0", "0", "0", "1", "5", "15", "36", "73", "131", "219", "344", "516", "746", "1044", "1424", "1899", "2483", "3193", "4044", "5055", "6245", "7633", "9240", "11088", "13200", "15600", "18313", "21365", "24783", "28596", "32833", "37523", "42699", "48392", "54636", "61466", "68916", "77024", "85827", "95363", "105673", "116796", "128775", "141653", "155473", "170280", "186120", "203040", "221088" ]	[ "easy", "nonn" ]	27	0	6	[ "A000332", "A011915", "A011933", "A052762" ]	null	N. J. A. Sloane	2024-11-03T09:34:05	oeisdata/seq/A011/A011933.seq	fa6ee194043cbeb7d3affcd5c02ffadb
A011934	a(n) = \|1^3 - 2^3 + 3^3 - 4^3 + ... + (-1)^(n+1)*n^3\|.	[ "0", "1", "7", "20", "44", "81", "135", "208", "304", "425", "575", "756", "972", "1225", "1519", "1856", "2240", "2673", "3159", "3700", "4300", "4961", "5687", "6480", "7344", "8281", "9295", "10388", "11564", "12825", "14175", "15616", "17152", "18785", "20519", "22356", "24300", "26353", "28519", "30800", "33200", "35721", "38367", "41140" ]	[ "nonn", "easy" ]	53	0	3	[ "A011934", "A015238", "A032528", "A153641" ]	null	David Penney (david(AT)math.uga.edu)	2024-11-03T09:33:53	oeisdata/seq/A011/A011934.seq	54ffee68df49d4ea8ed540d722cb77b9
A011935	a(n) = floor( n(n-1)(n-2)*(n-3)/25 ).	[ "0", "0", "0", "0", "0", "4", "14", "33", "67", "120", "201", "316", "475", "686", "960", "1310", "1747", "2284", "2937", "3720", "4651", "5745", "7022", "8500", "10200", "12144", "14352", "16848", "19656", "22800", "26308", "30206", "34521", "39283", "44520", "50265", "56548" ]	[ "nonn" ]	18	0	6	[ "A011915", "A011935" ]	null	N. J. A. Sloane	2025-01-18T13:46:18	oeisdata/seq/A011/A011935.seq	50991d4cd2260523a776b89875e444a2
A011936	a(n) = floor( n(n-1)(n-2)*(n-3)/26 ).	[ "0", "0", "0", "0", "0", "4", "13", "32", "64", "116", "193", "304", "456", "660", "924", "1260", "1680", "2196", "2824", "3577", "4472", "5524", "6752", "8173", "9808", "11676", "13800", "16200", "18900", "21924", "25296", "29044", "33193", "37772", "42808", "48332", "54373", "60964", "68136", "75924", "84360", "93480", "103320", "113916", "125308", "137533", "150632", "164644", "179612", "195577" ]	[ "nonn", "easy" ]	16	0	6	[ "A011915", "A011936" ]	null	N. J. A. Sloane	2024-10-29T03:43:53	oeisdata/seq/A011/A011936.seq	e67cc7f57bc6e62874e5e94ccdb15871
A011937	a(n) = floor( n(n-1)(n-2)*(n-3)/27 ).	[ "0", "0", "0", "0", "0", "4", "13", "31", "62", "112", "186", "293", "440", "635", "889", "1213", "1617", "2115", "2720", "3445", "4306", "5320", "6502", "7871", "9445", "11244", "13288", "15600", "18200", "21112", "24360", "27968", "31964", "36373", "41223", "46542", "52360", "58706", "65613", "73112", "81235", "90017", "99493", "109697", "120667", "132440", "145053", "158546", "172960", "188334" ]	[ "nonn", "easy" ]	19	0	6	[ "A011915", "A011937" ]	null	N. J. A. Sloane	2024-10-29T03:43:19	oeisdata/seq/A011/A011937.seq	6d634fb70fbb0eb1513ccedd9a6b8296
A011938	a(n) = floor( n(n-1)(n-2)*(n-3)/28 ).	[ "0", "0", "0", "0", "0", "4", "12", "30", "60", "108", "180", "282", "424", "612", "858", "1170", "1560", "2040", "2622", "3322", "4152", "5130", "6270", "7590", "9108", "10842", "12814", "15042", "17550", "20358", "23490", "26970", "30822", "35074", "39750", "44880", "50490", "56610", "63270", "70500", "78334", "86802", "95940", "105780" ]	[ "nonn", "easy" ]	26	0	6	[ "A011915", "A011938" ]	null	N. J. A. Sloane	2024-10-27T09:26:12	oeisdata/seq/A011/A011938.seq	679d62ac688a9d9492d8a55b2ff5f741
A011939	a(n) = floor( n(n-1)(n-2)*(n-3)/29 ).	[ "0", "0", "0", "0", "0", "4", "12", "28", "57", "104", "173", "273", "409", "591", "828", "1129", "1506", "1969", "2532", "3207", "4009", "4953", "6053", "7328", "8793", "10468", "12372", "14524", "16944", "19656", "22680", "26040", "29760", "33864", "38380", "43332", "48748", "54657", "61088", "68069", "75633", "83809", "92631", "102132", "112345", "123306", "135049", "147612", "161031", "175345" ]	[ "nonn", "easy" ]	20	0	6	[ "A011915", "A011939" ]	null	N. J. A. Sloane	2024-10-27T09:25:55	oeisdata/seq/A011/A011939.seq	ad410031d169d463e1c7983e4fc7f93e
A011940	a(n) = floor(n(n-1)(n-2)*(n-3)/30).	[ "0", "0", "0", "0", "0", "4", "12", "28", "56", "100", "168", "264", "396", "572", "800", "1092", "1456", "1904", "2448", "3100", "3876", "4788", "5852", "7084", "8500", "10120", "11960", "14040", "16380", "19000", "21924", "25172", "28768", "32736", "37100", "41888", "47124", "52836", "59052", "65800", "73112", "81016", "89544", "98728", "108600", "119196", "130548", "142692", "155664", "169500" ]	[ "nonn", "easy" ]	30	0	6	[ "A011795", "A011915", "A011940" ]	null	N. J. A. Sloane	2024-10-27T09:26:00	oeisdata/seq/A011/A011940.seq	e613ef1775475f96aaa30bcc94fbd7ac
A011941	a(n) = floor(n(n-1)(n-2)*(n-3)/31).	[ "0", "0", "0", "0", "0", "3", "11", "27", "54", "97", "162", "255", "383", "553", "774", "1056", "1409", "1842", "2369", "3000", "3750", "4633", "5663", "6855", "8226", "9793", "11574", "13587", "15851", "18387", "21216", "24360", "27840", "31680", "35904", "40536", "45603", "51131", "57147", "63678", "70753", "78402", "86655", "95543" ]	[ "nonn", "easy" ]	25	0	6	[ "A011915", "A011941" ]	null	N. J. A. Sloane	2024-10-27T03:13:19	oeisdata/seq/A011/A011941.seq	eddb7d297fcf0fab1c3e086d2fdd44f4
A011942	a(n) = floor( n(n-1)(n-2)*(n-3)/32 ).	[ "0", "0", "0", "0", "0", "3", "11", "26", "52", "94", "157", "247", "371", "536", "750", "1023", "1365", "1785", "2295", "2907", "3633", "4488", "5486", "6641", "7969", "9487", "11212", "13162", "15356", "17813", "20553", "23598", "26970", "30690", "34782", "39270", "44178", "49533", "55361", "61688", "68542", "75952", "83947", "92557", "101813", "111746", "122388", "133773", "145935", "158907", "172725" ]	[ "nonn", "easy" ]	20	0	6	[ "A011915", "A011942" ]	null	N. J. A. Sloane	2024-12-30T04:01:54	oeisdata/seq/A011/A011942.seq	d11ac7c0078f80e2d5dc390775e2fb89
A011943	Numbers k such that any group of k consecutive integers has integral standard deviation (viz. A011944(k)).	[ "1", "7", "97", "1351", "18817", "262087", "3650401", "50843527", "708158977", "9863382151", "137379191137", "1913445293767", "26650854921601", "371198523608647", "5170128475599457", "72010600134783751", "1002978273411373057", "13969685227624439047", "194572614913330773601", "2710046923559006391367" ]	[ "nonn", "easy" ]	103	1	2	[ "A000330", "A001075", "A007654", "A007655", "A011943", "A011944", "A102344", "A188644" ]	null	E. K. Lloyd	2025-02-06T08:21:05	oeisdata/seq/A011/A011943.seq	a11a3b05b83aac4c1359acd41a372cc7
A011944	a(n) = 14*a(n-1) - a(n-2) with a(0) = 0, a(1) = 2.	[ "0", "2", "28", "390", "5432", "75658", "1053780", "14677262", "204427888", "2847313170", "39657956492", "552364077718", "7693439131560", "107155783764122", "1492487533566148", "20787669686161950", "289534888072701152" ]	[ "nonn", "easy" ]	44	0	2	[ "A001353", "A007654", "A007655", "A011943", "A011944" ]	null	E. K. Lloyd	2022-06-06T08:07:59	oeisdata/seq/A011/A011944.seq	dbafb4a95d5a875acb266e713f6d51b8
A011945	Areas of almost-equilateral Heronian triangles (integral side lengths m-1, m, m+1 and integral area).	[ "0", "6", "84", "1170", "16296", "226974", "3161340", "44031786", "613283664", "8541939510", "118973869476", "1657092233154", "23080317394680", "321467351292366", "4477462600698444", "62363009058485850", "868604664218103456", "12098102289994962534", "168504827395711372020", "2346969481249964245746" ]	[ "nonn", "easy" ]	52	1	2	[ "A003500", "A007655", "A011945", "A016064", "A102341", "A103974", "A103975", "A334277", "A335025" ]	null	E. K. Lloyd	2025-02-16T08:32:32	oeisdata/seq/A011/A011945.seq	681d138eb9bea76f96413e33a35b7302
A011946	Number of Barlow packings with group P63/mmc(S) that repeat after 4n layers.	[ "1", "2", "3", "8", "15", "30", "63", "128", "252", "510", "1023", "2040", "4095", "8190", "16365", "32768", "65535", "131040", "262143", "524280", "1048509", "2097150", "4194303", "8388480", "16777200", "33554430", "67108608", "134217720", "268435455", "536870370", "1073741823", "2147483648", "4294966269", "8589934590" ]	[ "nonn", "easy" ]	43	1	2	[ "A000048", "A008683", "A011946", "A127804", "A195095" ]	null	N. J. A. Sloane	2024-04-15T07:30:33	oeisdata/seq/A011/A011946.seq	4fa0214d2eb0858924651039e4c7abc5
A011947	Number of Barlow packings with group P63/mmc(O) that repeat after 4n+2 layers.	[ "1", "1", "3", "7", "14", "31", "63", "123", "255", "511", "1015", "2047", "4092" ]	[ "nonn", "easy", "changed" ]	15	0	3	null	null	N. J. A. Sloane	2025-07-08T02:43:05	oeisdata/seq/A011/A011947.seq	d08dba568086a36aba5da3bcacb2e7ac
A011948	Number of Barlow packings with group P63mc that repeat after 2n layers.	[ "1", "1", "4", "7", "18", "31", "70", "126", "261", "484", "960", "1800", "3514", "6643", "12852", "24457", "47151", "90157", "173740", "333498", "643230", "1238664", "2392650", "4620006", "8939657", "17302033", "33538048", "65042495", "126289800", "245361171", "477153040", "928510506", "1808276211", "3523813566", "6871685532", "13408154100", "26178323928", "51139027135" ]	[ "nonn" ]	24	6	3	[ "A011948", "A045668", "A309784" ]	null	N. J. A. Sloane	2024-04-15T06:58:57	oeisdata/seq/A011/A011948.seq	38611693f8816e895bd385d1f74cbcce
A011949	Number of Barlow packings with group P6(bar)m2 that repeat after 2n layers.	[ "0", "0", "1", "2", "6", "12", "28", "56", "119", "240", "496", "990", "2016", "4032", "8121", "16256", "32640", "65268", "130816", "261630", "523747", "1047552", "2096128", "4192200", "8386554", "16773120", "33550216", "67100670", "134209536", "268418820", "536854528", "1073709056", "2147450383", "4294901760", "8589869022", "17179737120", "34359607296" ]	[ "nonn", "easy", "changed" ]	13	1	4	null	null	N. J. A. Sloane	2025-07-08T02:43:12	oeisdata/seq/A011/A011949.seq	4d21414b4baed79d5c5dbce65db7c2b8
A011950	Number of Barlow packings with group P3(bar)m1(SO) that repeat after 2n-1 layers.	[ "0", "0", "1", "3", "3", "11", "21", "39", "85", "171", "333", "683", "1364", "2715", "5461", "10923", "21813", "43687", "87381", "174699", "349525", "699051", "1397970", "2796203", "5592402", "11184555", "22369621", "44739231", "89477973", "178956971", "357913941", "715826856", "1431655743", "2863311531", "5726621013", "11453246123" ]	[ "nonn", "easy", "changed" ]	20	1	4	null	null	N. J. A. Sloane	2025-07-08T02:43:17	oeisdata/seq/A011/A011950.seq	2eb14d8e2b9def34a696c1ac684e2e40
A011951	Number of Barlow packings with group P3(bar)m1(S) that repeat after 2n layers.	[ "0", "0", "0", "0", "2", "3", "9", "16", "39", "75", "165", "318", "672", "1323", "2703", "5376", "10880", "21663", "43605", "87040", "174564", "348843", "698709", "1396680", "2795518", "5589675", "11183325", "22364160", "44736512", "89467320", "178951509", "357892096", "715816464", "1431612075", "2863289674", "5726534688", "11453202432" ]	[ "nonn", "easy", "changed" ]	21	1	5	null	null	N. J. A. Sloane	2025-07-08T02:43:24	oeisdata/seq/A011/A011951.seq	ad4da0bfc3b95bef067da5e14bcc1f0f
A011952	Number of Barlow packings with group P3(bar)m1(O) that repeat after 2n layers.	[ "2", "3", "8", "16", "40", "73", "165", "320", "666", "1323", "2709", "5364", "10880", "21675", "43577", "87040", "174590", "348787", "698709", "1396736", "2795400", "5589672", "11183445", "22363920", "44736510", "89467563", "178951005", "357892096", "715816960", "1431611083", "2863289685", "5726535661", "11453200416" ]	[ "nonn", "easy", "changed" ]	13	4	1	null	null	N. J. A. Sloane	2025-07-08T02:43:30	oeisdata/seq/A011/A011952.seq	d9dc0f2bcda36f1c50df75311ec70c70
A011953	Number of Barlow packings with group P3m1 that repeat after n layers.	[ "3", "2", "10", "15", "42", "68", "162", "280", "600", "1088", "2214", "4112", "8154", "15366", "30052", "57208", "111166", "212982", "412890", "794688", "1540002", "2974150", "5767344", "11167872", "21680832", "42073640", "81787057", "159005154", "309503502", "602667098" ]	[ "nonn", "easy", "changed" ]	9	9	1	null	null	N. J. A. Sloane	2025-07-08T02:43:36	oeisdata/seq/A011/A011953.seq	6c51e7a57edc1d01f3b518d14e4daf39
A011954	Barlow packings with group R3(bar)m(SO) that repeat after 6n+3 layers.	[ "1", "1", "2", "4", "11", "20", "42", "84", "170", "340", "682", "1364", "2728", "5461", "10922", "21844", "43690", "87374", "174762", "349524", "699050", "1398100", "2796192", "5592404", "11184806", "22369620", "44739242", "89478462", "178956970", "357913940", "715827882", "1431655754", "2863311486", "5726623060", "11453246122", "22906492244", "45812984490" ]	[ "nonn", "easy", "changed" ]	15	0	3	null	null	N. J. A. Sloane	2025-07-08T02:43:42	oeisdata/seq/A011/A011954.seq	21cee2a40e3e28989f20905c9ad14039
A011955	Number of Barlow packings with group R3(bar)m(O) that repeat after 6n layers.	[ "1", "2", "4", "9", "19", "40", "80", "165", "330", "672", "1344", "2709", "5418", "10878", "21760", "43605", "87211", "174592", "349180", "698707", "1397418", "2795520", "5591040", "11183436", "22366890", "44736512", "89473020", "178951509", "357903000", "715816960", "1431633920", "2863289683", "5726579370", "11453202383", "22906404864", "45812897109", "91625794218" ]	[ "nonn", "easy", "changed" ]	19	2	2	null	null	N. J. A. Sloane	2025-07-08T02:43:49	oeisdata/seq/A011/A011955.seq	f774e62eba40bdba3a6634943c7026e9
A011956	Number of close-packings with layer-number 3n and space group R3m.	[ "1", "2", "4", "10", "21", "42", "84", "164", "322", "620", "1200", "2300", "4429", "8482", "16303", "31259", "60105", "115472", "222332", "428106", "825774", "1593669", "3080004", "5956902", "11534689", "22352962", "43361663", "84181720", "163574114", "318079104", "619007004", "1205471654", "2349209058", "4581032192" ]	[ "nonn", "easy" ]	30	7	2	[ "A011768", "A011954", "A011955", "A011956", "A371992" ]	null	N. J. A. Sloane	2025-06-18T00:56:13	oeisdata/seq/A011/A011956.seq	f7af2159ec76bc9aaaca06cd82abd631
A011957	Number of ZnS polytypes that repeat after n layers.	[ "0", "1", "1", "1", "1", "2", "3", "6", "10", "18", "31", "59", "105", "198", "365", "688", "1285", "2438", "4599", "8755", "16647", "31806", "60787", "116570", "223696", "430290", "828514", "1598025", "3085465", "5965612", "11545611", "22370304", "43383539", "84216330", "163617801", "318148208", "619094385", "1205609454", "2349383925", "4581307186", "8939118925", "17452582356" ]	[ "nonn", "easy" ]	52	1	6	[ "A000048", "A011957", "A165920", "A165921" ]	null	N. J. A. Sloane	2019-12-05T04:21:08	oeisdata/seq/A011/A011957.seq	2a843be4e9974e9d108eb1ba563e8c91
A011958	Number of CdI_2 polytypes that repeat after 2n layers.	[ "1", "1", "3", "8", "22", "68", "216", "728", "2513", "8920", "32116", "117240", "431550", "1600734", "5970704", "22381184", "84236890", "318191804", "1205692236", "4581481776", "17452915218", "66637798834", "254960616136", "977346581800", "3753005281872" ]	[ "nonn", "easy", "changed" ]	7	1	3	null	null	N. J. A. Sloane	2025-07-08T02:43:55	oeisdata/seq/A011/A011958.seq	77936621c910fddbdf013687c5bf806e
A011959	Number of SiC polytypes that repeat after 2n layers.	[ "0", "0", "1", "1", "0", "1", "1", "1", "1", "3", "3", "4", "7", "11", "15", "24", "36", "55", "81", "129", "195", "301", "465", "728", "1116", "1745", "2717", "4239", "6603", "10357", "16189", "25383", "39807", "62557", "98245", "154608", "243346", "383436", "604346", "953582", "1505106", "2377442", "3757050", "5941269" ]	[ "nonn", "easy", "changed" ]	7	1	10	null	null	N. J. A. Sloane	2025-07-08T02:44:01	oeisdata/seq/A011/A011959.seq	2665531bf72b82afe2e478770e37d81e
A011960	Number of ferrites M_2Y_n that repeat after 6n+10 layers.	[ "0", "1", "1", "1", "1", "2", "1", "2", "2", "2", "2", "3", "2", "3", "3", "3", "3", "4", "3", "4" ]	[ "nonn", "more" ]	13	1	6	null	null	N. J. A. Sloane	2021-05-20T00:23:18	oeisdata/seq/A011/A011960.seq	9a439e7f2ed0caff98eaf2dbfb1785fa
A011961	Number of ferrites M_4Y_n that repeat after 6n+20 layers.	[ "0", "1", "2", "2", "3", "6", "6", "9", "13", "15", "18", "25", "27", "34", "42", "47", "54", "67", "72", "84" ]	[ "nonn", "easy", "changed" ]	7	1	3	null	null	N. J. A. Sloane	2025-07-08T02:44:07	oeisdata/seq/A011/A011961.seq	82245a646aa180164e411865c2791c99
A011962	Number of ferrites M_6Y_n that repeat after 6n+30 layers.	[ "0", "2", "3", "6", "9", "19", "24", "46", "62", "96", "132", "194", "249", "354", "452", "600", "762", "986", "1212", "1544" ]	[ "nonn", "easy", "changed" ]	7	1	2	null	null	N. J. A. Sloane	2025-07-08T02:44:13	oeisdata/seq/A011/A011962.seq	11bfd67a658037113300d49d89e9d195
A011963	Number of ferrites M_8Y_n that repeat after 6n+40 layers.	[ "0", "2", "4", "10", "19", "44", "76", "150", "251", "432", "686", "1094", "1646", "2498", "3608", "5206", "7301", "10160", "13814", "18718" ]	[ "nonn", "easy", "changed" ]	7	1	2	null	null	N. J. A. Sloane	2025-07-08T02:44:18	oeisdata/seq/A011/A011963.seq	379f4232508857bafedf45b7021eb999
A011964	Number of ferrites M_{10}Y_n that repeat after 6n+50 layers.	[ "0", "3", "5", "18", "38", "100", "198", "445", "829", "1605", "2851", "5014", "8361", "13843", "21907", "34362", "52327", "78571", "115434", "167695" ]	[ "nonn", "easy", "changed" ]	7	1	2	null	null	N. J. A. Sloane	2025-07-08T02:44:25	oeisdata/seq/A011/A011964.seq	01dd5795964858ab29899adc97e2f62b
A011965	Second differences of Bell numbers.	[ "1", "2", "7", "27", "114", "523", "2589", "13744", "77821", "467767", "2972432", "19895813", "139824045", "1028804338", "7905124379", "63287544055", "526827208698", "4551453462543", "40740750631417", "377254241891064", "3608700264369193", "35613444194346451", "362161573323083920", "3790824599495473121" ]	[ "nonn", "easy" ]	96	0	2	[ "A000110", "A005493", "A006014", "A011965", "A090365", "A106436", "A124758", "A217924", "A243499", "A284005", "A290615", "A329369", "A341392", "A347204", "A347205", "A350309" ]	null	N. J. A. Sloane	2025-01-22T11:37:47	oeisdata/seq/A011/A011965.seq	5cb1872970aab4e6ce22d96433a98263
A011966	Third differences of Bell numbers.	[ "1", "5", "20", "87", "409", "2066", "11155", "64077", "389946", "2504665", "16923381", "119928232", "888980293", "6876320041", "55382419676", "463539664643", "4024626253845", "36189297168874", "336513491259647", "3231446022478129", "32004743929977258", "326548129128737469", "3428663026172389201" ]	[ "nonn" ]	42	0	2	[ "A000110", "A005493", "A011965", "A011966", "A106436" ]	null	N. J. A. Sloane	2025-02-04T11:37:44	oeisdata/seq/A011/A011966.seq	3ba597505c7d822c863d325848f440d9
A011967	4th differences of Bell numbers.	[ "4", "15", "67", "322", "1657", "9089", "52922", "325869", "2114719", "14418716", "103004851", "769052061", "5987339748", "48506099635", "408157244967", "3561086589202", "32164670915029", "300324194090773", "2894932531218482", "28773297907499129" ]	[ "nonn" ]	23	0	1	[ "A000110", "A005493", "A011965", "A011966", "A011967", "A106436" ]	null	N. J. A. Sloane	2025-02-13T01:30:13	oeisdata/seq/A011/A011967.seq	2aed2a25f1f53205a23039f10db7fe64
A011968	Apply (1+Shift) to Bell numbers.	[ "1", "2", "3", "7", "20", "67", "255", "1080", "5017", "25287", "137122", "794545", "4892167", "31858034", "218543759", "1573857867", "11863100692", "93345011951", "764941675963", "6514819011216", "57556900440429", "526593974392123", "4981585554604074", "48658721593531669", "490110875149889635" ]	[ "nonn" ]	85	0	2	[ "A000110", "A000296", "A000569", "A011968", "A011969", "A011970", "A011971", "A106436", "A240936", "A321750" ]	null	N. J. A. Sloane	2025-02-13T01:30:09	oeisdata/seq/A011/A011968.seq	67476641b18934a10235550caaacccde
A011969	Apply (1+Shift)^2 to Bell numbers.	[ "1", "3", "5", "10", "27", "87", "322", "1335", "6097", "30304", "162409", "931667", "5686712", "36750201", "250401793", "1792401626", "13436958559", "105208112643", "858286687914", "7279760687179", "64071719451645", "584150874832552", "5508179528996197" ]	[ "nonn" ]	79	0	2	[ "A000110", "A011968", "A011969", "A011970", "A011971", "A106436" ]	null	N. J. A. Sloane	2025-04-04T01:16:42	oeisdata/seq/A011/A011969.seq	43307c591c826cdb58fec88643b3e441
A011970	Apply (1+Shift)^3 to Bell numbers.	[ "1", "4", "8", "15", "37", "114", "409", "1657", "7432", "36401", "192713", "1094076", "6618379", "42436913", "287151994", "2042803419", "15229360185", "118645071202", "963494800557", "8138047375093", "71351480138824", "648222594284197", "6092330403828749" ]	[ "nonn", "changed" ]	41	0	2	[ "A000110", "A011968", "A011969", "A011970", "A011971", "A106436" ]	null	N. J. A. Sloane	2025-07-08T02:44:31	oeisdata/seq/A011/A011970.seq	568a8fbc182ee9d28031c4a921e61e71
A011971	Aitken's array: triangle of numbers {a(n,k), n >= 0, 0 <= k <= n} read by rows, defined by a(0,0)=1, a(n,0) = a(n-1,n-1), a(n,k) = a(n,k-1) + a(n-1,k-1).	[ "1", "1", "2", "2", "3", "5", "5", "7", "10", "15", "15", "20", "27", "37", "52", "52", "67", "87", "114", "151", "203", "203", "255", "322", "409", "523", "674", "877", "877", "1080", "1335", "1657", "2066", "2589", "3263", "4140", "4140", "5017", "6097", "7432", "9089", "11155", "13744", "17007", "21147", "21147", "25287", "30304", "36401", "43833", "52922", "64077", "77821", "94828", "115975" ]	[ "tabl", "nonn", "easy", "nice" ]	132	0	3	[ "A000110", "A005493", "A011965", "A011966", "A011968", "A011969", "A011971", "A011972", "A046934", "A094577", "A095149", "A106436", "A108041", "A108042", "A108043", "A123346" ]	null	N. J. A. Sloane, J. H. Conway and R. K. Guy	2025-02-16T08:32:32	oeisdata/seq/A011/A011971.seq	63ecc87aa7951aa78c66a929cbfc5ef6
A011972	Sequence formed by reading rows of triangle defined in A011971.	[ "1", "2", "3", "5", "7", "10", "15", "20", "27", "37", "52", "67", "87", "114", "151", "203", "255", "322", "409", "523", "674", "877", "1080", "1335", "1657", "2066", "2589", "3263", "4140", "5017", "6097", "7432", "9089", "11155", "13744", "17007", "21147", "25287", "30304", "36401", "43833", "52922", "64077", "77821", "94828" ]	[ "nonn", "easy", "tabl" ]	30	0	2	null	null	N. J. A. Sloane and J. H. Conway	2023-12-02T05:09:49	oeisdata/seq/A011/A011972.seq	1fc9dc186adebfb754241a1c4be241cf
A011973	Irregular triangle read by rows: T(n,k) = binomial(n-k, k), n >= 0, 0 <= k <= floor(n/2); or, coefficients of (one version of) Fibonacci polynomials.	[ "1", "1", "1", "1", "1", "2", "1", "3", "1", "1", "4", "3", "1", "5", "6", "1", "1", "6", "10", "4", "1", "7", "15", "10", "1", "1", "8", "21", "20", "5", "1", "9", "28", "35", "15", "1", "1", "10", "36", "56", "35", "6", "1", "11", "45", "84", "70", "21", "1", "1", "12", "55", "120", "126", "56", "7", "1", "13", "66", "165", "210", "126", "28", "1", "1", "14", "78", "220", "330", "252", "84", "8", "1", "15", "91", "286", "495", "462" ]	[ "tabf", "easy", "nonn", "nice" ]	337	0	6	[ "A000045", "A000108", "A000129", "A000930", "A007318", "A011973", "A025581", "A030528", "A049310", "A052553", "A053122", "A053123", "A054123", "A054142", "A055087", "A055151", "A092865", "A098474", "A098925", "A102426", "A124644", "A134264", "A169803", "A332602" ]	null	N. J. A. Sloane	2025-02-16T08:32:32	oeisdata/seq/A011/A011973.seq	5bd6453daf9116ce4e1d49e8cbbc0f5a
A011974	2 followed by the numbers that are the sum of 2 successive primes.	[ "2", "5", "8", "12", "18", "24", "30", "36", "42", "52", "60", "68", "78", "84", "90", "100", "112", "120", "128", "138", "144", "152", "162", "172", "186", "198", "204", "210", "216", "222", "240", "258", "268", "276", "288", "300", "308", "320", "330", "340", "352", "360", "372", "384", "390", "396", "410", "434", "450", "456", "462", "472", "480", "492", "508", "520" ]	[ "nonn", "easy" ]	22	1	1	[ "A000040", "A011974" ]	null	N. J. A. Sloane	2022-06-25T12:53:39	oeisdata/seq/A011/A011974.seq	83f043d2db2300e48f04794bb26931e7
A011975	Covering numbers C(n,3,2).	[ "1", "3", "4", "6", "7", "11", "12", "17", "19", "24", "26", "33", "35", "43", "46", "54", "57", "67", "70", "81", "85", "96", "100", "113", "117", "131", "136", "150", "155", "171", "176", "193", "199", "216", "222", "241", "247", "267", "274", "294", "301", "323", "330", "353", "361", "384", "392", "417", "425", "451", "460", "486" ]	[ "nonn", "easy" ]	32	3	2	[ "A001839", "A011975", "A011976", "A011977", "A036838", "A066010" ]	null	N. J. A. Sloane	2024-01-10T20:13:00	oeisdata/seq/A011/A011975.seq	6ce98c7ced0f8fab47627e3ad782bf1b
A011976	Covering numbers C(n,4,2).	[ "1", "3", "3", "5", "6", "8", "9", "11", "12", "13", "18", "19", "20", "26", "27", "31", "35", "37", "39", "46", "48", "50", "59", "61", "63", "73", "75", "78", "88", "91", "94", "105", "108", "111", "124", "127", "130", "144", "147", "151", "165", "169", "173", "188", "192", "196", "213", "217", "221", "239", "243", "248", "266", "271", "276", "295", "300", "305", "326" ]	[ "nonn", "easy", "changed" ]	16	4	2	[ "A011975", "A011976", "A011977" ]	null	N. J. A. Sloane	2025-07-08T02:44:39	oeisdata/seq/A011/A011976.seq	198740203f6b65cc97c73ecd51d7a871
A011977	Covering numbers C(n,5,2).	[ "1", "3", "3", "4", "5", "6", "7", "9", "10", "12", "13", "15", "16", "18", "19", "21", "21", "27", "28", "30", "30", "37", "38", "40" ]	[ "nonn", "hard", "changed" ]	16	5	2	[ "A011975", "A011977", "A240116" ]	null	N. J. A. Sloane	2025-07-08T02:44:47	oeisdata/seq/A011/A011977.seq	7f68d8ddb0c7b0f2db8adc405eeff43d
A011978	Covering numbers C(n,6,2).	[ "1", "3", "3", "3", "4", "6", "6", "7", "7", "10", "10", "12", "12", "15", "16", "17", "19" ]	[ "nonn", "hard", "more" ]	12	6	2	null	null	N. J. A. Sloane	2023-09-21T16:57:32	oeisdata/seq/A011/A011978.seq	40c1f2f9a8e79520f03e3dbc51c0e7a6
A011979	Covering numbers C(n,4,3) (next term is <= 261).	[ "1", "4", "6", "12", "14", "25", "30", "47", "57", "78", "91", "124", "140", "183", "207" ]	[ "nonn", "hard" ]	13	4	2	[ "A011979", "A066010" ]	null	N. J. A. Sloane	2020-02-02T21:33:55	oeisdata/seq/A011/A011979.seq	3c95faeb745c71363030096e5c0f6f83
A011980	Covering numbers C(n,5,3) (next term is <= 29).	[ "1", "4", "5", "8", "12", "17", "20" ]	[ "nonn", "hard", "changed" ]	11	5	2	null	null	N. J. A. Sloane	2025-07-08T02:44:53	oeisdata/seq/A011/A011980.seq	5ba2a857b1cc3b8da336934c9f3eed48
A011981	Covering numbers C(n,6,3) (next term is <= 21).	[ "1", "4", "4", "7", "10", "11", "15" ]	[ "nonn", "hard", "changed" ]	11	6	2	null	null	N. J. A. Sloane	2025-07-08T02:45:00	oeisdata/seq/A011/A011981.seq	545bb67ee421b96614a110f57770bcae
A011982	Covering numbers C(n,7,3) (next term is <= 25).	[ "1", "4", "4", "6", "8", "11", "13", "14", "15" ]	[ "nonn", "hard", "changed" ]	11	7	2	null	null	N. J. A. Sloane	2025-07-08T02:45:06	oeisdata/seq/A011/A011982.seq	daf2ed0b8989ffd5f368c0ffc9a9ce51
A011983	Covering numbers C(n,5,4).	[ "1", "5", "9", "20", "30", "51", "66", "113" ]	[ "nonn", "hard" ]	19	5	2	[ "A011983", "A066009", "A066010" ]	null	N. J. A. Sloane	2023-08-24T13:42:22	oeisdata/seq/A011/A011983.seq	23164c31451b69d2380e9c05f0442e3e
A011984	Covering numbers C(n,6,4) (next term is <= 41).	[ "5", "7", "12", "20", "32" ]	[ "nonn", "more", "hard", "changed" ]	15	6	1	null	null	N. J. A. Sloane	2025-07-08T02:45:12	oeisdata/seq/A011/A011984.seq	0b230700b8f3cebb17c27fc49c9fde81
A011985	Covering numbers C(n,7,4) (next term is <= 24).	[ "1", "5", "6", "10", "17" ]	[ "nonn", "hard", "changed" ]	11	7	2	null	null	N. J. A. Sloane	2025-07-08T02:45:19	oeisdata/seq/A011/A011985.seq	7bfe27de9b36e0bc01ccff36b8e8d57d
A011986	Covering numbers C(n,7,4) (next term is <= 19).	[ "1", "5", "5", "9", "12" ]	[ "nonn", "hard", "changed" ]	11	8	2	null	null	N. J. A. Sloane	2025-07-08T02:45:25	oeisdata/seq/A011/A011986.seq	5656ed38ed9ef0e450da58ca33db7a0b
A011987	Covering numbers C(n,6,5) (next term is <= 100).	[ "1", "6", "12", "30", "50" ]	[ "nonn", "hard" ]	13	6	2	[ "A011987", "A066010" ]	null	N. J. A. Sloane	2020-02-02T21:33:25	oeisdata/seq/A011/A011987.seq	442ffcb7e0a3611923ebb6576eaa2304
A011988	Covering numbers C(n,7,5) (next term is <= 34).	[ "1", "6", "9", "20" ]	[ "nonn", "hard", "changed" ]	11	7	2	null	null	N. J. A. Sloane	2025-07-08T02:45:31	oeisdata/seq/A011/A011988.seq	16aeba958eb8229fa41ec58e90acc669
A011989	Covering numbers C(n,8,5) (next term is <= 43).	[ "1", "6", "8", "16", "26" ]	[ "nonn", "hard", "changed" ]	11	8	2	null	null	N. J. A. Sloane	2025-07-08T02:45:39	oeisdata/seq/A011/A011989.seq	0eddcbfe6d65e95c2001bf10d028dd74
A011990	Covering numbers C(n,9,5) (next term is <= 19).	[ "1", "6", "7", "12" ]	[ "nonn", "hard" ]	12	9	2	null	null	N. J. A. Sloane	2019-12-30T15:08:51	oeisdata/seq/A011/A011990.seq	589db526c7f337598af5a23e6cd88b56
A011991	(n,3,1) difference families over Z_n.	[ "1", "0", "0", "0", "0", "0", "1", "0", "2", "0", "0", "0", "4", "0", "7", "0", "0", "0", "12", "0", "8", "0", "0", "0", "80", "0", "84", "0", "0", "0", "820", "0", "798", "0", "0", "0", "9508", "0", "11616", "0", "0", "0", "157340", "0", "139828", "0", "0", "0", "3027456", "0", "2353310" ]	[ "nonn", "changed" ]	6	7	9	null	null	N. J. A. Sloane	2025-07-08T02:45:44	oeisdata/seq/A011/A011991.seq	056b61516b2f5079527c02aba0aed2b2
A011992	(n,3,2) difference families over Z_n.	[ "2", "0", "0", "0", "0", "4", "9", "0", "9", "71", "0", "0", "201", "0", "175", "0", "0", "2939", "19543", "0", "10841", "609483" ]	[ "nonn", "hard", "changed" ]	6	7	1	null	null	N. J. A. Sloane	2025-07-08T02:46:04	oeisdata/seq/A011/A011992.seq	4f3809dec28ab1cc473d7d2d08e0fa41
A011993	(2n+1,3,3) difference families over Z_{2n+1}.	[ "1", "3", "4", "8", "47", "421", "1550", "13316", "212968" ]	[ "nonn", "hard", "changed" ]	6	2	2	null	null	N. J. A. Sloane	2025-07-08T02:46:10	oeisdata/seq/A011/A011993.seq	f9dcaa8431149e4c357d795cfecbf358
A011994	(n,3,4) difference families over Z_n.	[ "2", "4", "0", "3", "21", "0", "180", "253", "0", "2981", "21742", "0", "320760" ]	[ "nonn", "hard", "changed" ]	6	6	1	null	null	N. J. A. Sloane	2025-07-08T02:46:17	oeisdata/seq/A011/A011994.seq	9e4356a08f97f26d2fa275ed594dd2a9
A011995	(n,3,5) difference families over Z_n.	[ "5", "0", "4", "0", "0", "0", "1224", "0", "15686", "0", "0", "0" ]	[ "nonn", "hard", "changed" ]	6	7	1	null	null	N. J. A. Sloane	2025-07-08T02:46:22	oeisdata/seq/A011/A011995.seq	786d929e5491d8be3103054df4109970
A011996	(n,3,6) difference families over Z_n.	[ "1", "0", "7", "12", "24", "0", "209", "3561", "5285", "0", "375372", "2460490" ]	[ "nonn", "hard", "changed" ]	6	5	3	null	null	N. J. A. Sloane	2025-07-08T02:46:29	oeisdata/seq/A011/A011996.seq	eb579b9157e774997cf403fa9f889491
A011997	Number of (n,3,7) difference families over Z_n.	[ "8", "0", "27", "0", "0", "0", "20347", "0" ]	[ "nonn", "hard", "changed" ]	7	7	1	null	null	N. J. A. Sloane	2025-07-08T02:46:35	oeisdata/seq/A011/A011997.seq	37765a9a747e89c60aff2d32eb936d80
A011998	(n,3,8) difference families over Z_n.	[ "3", "10", "0", "30", "360", "0", "15264", "70924", "0" ]	[ "nonn", "hard", "changed" ]	6	6	1	null	null	N. J. A. Sloane	2025-07-08T02:46:41	oeisdata/seq/A011/A011998.seq	3b068b52398568106dc0ee98487e48c8
A011999	(2n+1,3,9) difference families over Z_{2n+1}.	[ "1", "12", "108", "2593", "225900" ]	[ "nonn", "hard", "changed" ]	6	2	2	null	null	N. J. A. Sloane	2025-07-08T02:46:47	oeisdata/seq/A011/A011999.seq	9ac8525cc52bb15ff0399d1074eb723b
A012000	Expansion of 1/sqrt(1 - 4x + 16x^2).	[ "1", "2", "-2", "-28", "-74", "92", "1324", "3656", "-4826", "-70228", "-197372", "267896", "3921724", "11126936", "-15347432", "-225505648", "-643622906", "897078476", "13214495764", "37869162392", "-53170602284", "-784672445368", "-2255295815192", "3183829452272", "47051201187676", "135537088268792", "-192142210448216" ]	[ "sign" ]	68	0	2	[ "A012000", "A098332", "A116091", "A126869" ]	null	Wouter Meeussen	2021-12-04T12:25:07	oeisdata/seq/A012/A012000.seq	0ab012f66018817a82aef290ad04008f

A011901

a(n) = floor( n*(n-1)*(n-2)/19 ).

[ "0", "0", "0", "0", "1", "3", "6", "11", "17", "26", "37", "52", "69", "90", "114", "143", "176", "214", "257", "306", "360", "420", "486", "559", "639", "726", "821", "923", "1034", "1153", "1282", "1419", "1566", "1722", "1889", "2066", "2254", "2453", "2664", "2886", "3120", "3366", "3625", "3897", "4182", "4481", "4793", "5120", "5461", "5818", "6189", "6576", "6978", "7397", "7832", "8284", "8753", "9240", "9744", "10266", "10806", "11365", "11943", "12540", "13157", "13793", "14450", "15127" ]

[ "nonn", "easy" ]

33

0

6

[ "A011886", "A011901" ]

null

N. J. A. Sloane

2025-02-01T19:54:37

oeisdata/seq/A011/A011901.seq

a9cc74f34c9355795c9a5f36f3c9c170

A011902

a(n) = floor( n*(n-1)*(n-2)/20 ).

[ "0", "0", "0", "0", "1", "3", "6", "10", "16", "25", "36", "49", "66", "85", "109", "136", "168", "204", "244", "290", "342", "399", "462", "531", "607", "690", "780", "877", "982", "1096", "1218", "1348", "1488", "1636", "1795", "1963", "2142", "2331", "2530", "2741", "2964", "3198", "3444", "3702", "3973", "4257", "4554", "4864", "5188", "5527", "5880", "6247", "6630", "7027", "7441", "7870", "8316", "8778", "9256", "9752", "10266", "10797", "11346", "11913", "12499", "13104", "13728", "14371" ]

[ "nonn", "easy" ]

22

0

6

[ "A011886", "A011902" ]

null

N. J. A. Sloane

2024-10-18T06:08:35

oeisdata/seq/A011/A011902.seq

3db55d2640963b5240c58ce76c81370a

A011903

a(n) = floor(n*(n-1)*(n-2)/21).

[ "0", "0", "0", "0", "1", "2", "5", "10", "16", "24", "34", "47", "62", "81", "104", "130", "160", "194", "233", "276", "325", "380", "440", "506", "578", "657", "742", "835", "936", "1044", "1160", "1284", "1417", "1558", "1709", "1870", "2040", "2220", "2410", "2611", "2822", "3045", "3280" ]

[ "nonn", "easy" ]

27

0

6

[ "A011886", "A011903" ]

null

N. J. A. Sloane

2024-10-18T01:19:47

oeisdata/seq/A011/A011903.seq

2c1159a6ed72b0d42ac955ac0693cc56

A011904

a(n) = floor( n*(n-1)*(n-2)/22 ).

[ "0", "0", "0", "0", "1", "2", "5", "9", "15", "22", "32", "45", "60", "78", "99", "124", "152", "185", "222", "264", "310", "362", "420", "483", "552", "627", "709", "797", "893", "996", "1107", "1225", "1352", "1488", "1632", "1785", "1947", "2119", "2300", "2492", "2694", "2907", "3130", "3365", "3612", "3870", "4140", "4422", "4717", "5024", "5345", "5679", "6027", "6388", "6764", "7155", "7560", "7980", "8415", "8866", "9332", "9815", "10314", "10830", "11362", "11912", "12480", "13065", "13668" ]

[ "nonn", "easy" ]

24

0

6

[ "A011886", "A011904" ]

null

N. J. A. Sloane

2024-10-18T06:08:35

oeisdata/seq/A011/A011904.seq

ee74c93d8ad679aa5fdc3e4a7de7e408

A011905

a(n) = floor( n*(n-1)*(n-2)/23 ).

[ "0", "0", "0", "0", "1", "2", "5", "9", "14", "21", "31", "43", "57", "74", "94", "118", "146", "177", "212", "252", "297", "346", "401", "462", "528", "600", "678", "763", "854", "953", "1059", "1172", "1293", "1423", "1561", "1707", "1862", "2026", "2200", "2384", "2577", "2780", "2994", "3219", "3454", "3701", "3960", "4230", "4512", "4806", "5113", "5432", "5765", "6111", "6470", "6843", "7231", "7633", "8049", "8480", "8926", "9388", "9866", "10359", "10868", "11394", "11937", "12496", "13073" ]

[ "nonn", "easy" ]

22

0

6

[ "A011886", "A011905" ]

null

N. J. A. Sloane

2024-10-18T06:08:35

oeisdata/seq/A011/A011905.seq

7a9c2e2b1c810085307ca3749d90187b

A011906

If b(n) is A011900(n) and c(n) is A001109(n), then a(n) = b(n)*c(n) = b(n) + (b(n)+1) + (b(n)+2) + ... + c(n).

[ "1", "18", "525", "17340", "586177", "19896030", "675781821", "22956120408", "779829016225", "26491211221770", "899921240562957", "30570830315362260", "1038508305678375841", "35278711540581704598", "1198437683944896688125", "40711602541832856049200", "1382996048733983114022337" ]

[ "nonn", "easy" ]

30

1

2

[ "A001109", "A011900", "A011906", "A029547", "A091761" ]

null

Mario Velucchi (mathchess(AT)velucchi.it)

2024-10-18T06:08:52

oeisdata/seq/A011/A011906.seq

9b98ee8837ea3ff90f5e9994ce8e91bd

A011907

a(n) = floor( n*(n-1)*(n-2)/25 ).

[ "0", "0", "0", "0", "0", "2", "4", "8", "13", "20", "28", "39", "52", "68", "87", "109", "134", "163", "195", "232", "273", "319", "369", "425", "485", "552", "624", "702", "786", "876", "974", "1078", "1190", "1309", "1436", "1570", "1713", "1864", "2024", "2193", "2371", "2558", "2755", "2961", "3178", "3405", "3643", "3891", "4151", "4421", "4704", "4998", "5304", "5622", "5952", "6296", "6652", "7022", "7405", "7802", "8212", "8637", "9076", "9530", "9999", "10483", "10982", "11497", "12027" ]

[ "nonn", "easy" ]

18

0

6

[ "A011886", "A011907" ]

null

N. J. A. Sloane

2024-10-18T06:09:22

oeisdata/seq/A011/A011907.seq

b3f902d52eeca675231803d87b655abc

A011908

a(n) = floor( n*(n-1)*(n-2)/26 ).

[ "0", "0", "0", "0", "0", "2", "4", "8", "12", "19", "27", "38", "50", "66", "84", "105", "129", "156", "188", "223", "263", "306", "355", "408", "467", "530", "600", "675", "756", "843", "936", "1037", "1144", "1259", "1380", "1510", "1647", "1793", "1946", "2109", "2280", "2460", "2649", "2847", "3056", "3274", "3503", "3741", "3991", "4251", "4523", "4805", "5100", "5406", "5724", "6054", "6396", "6752", "7120" ]

[ "nonn" ]

19

0

6

[ "A011886", "A011908" ]

null

N. J. A. Sloane

2024-10-18T06:29:57

oeisdata/seq/A011/A011908.seq

b87a102d9573125606119b51ed1ab205

A011909

a(n) = floor( n*(n-1)*(n-2)/27 ).

[ "0", "0", "0", "0", "0", "2", "4", "7", "12", "18", "26", "36", "48", "63", "80", "101", "124", "151", "181", "215", "253", "295", "342", "393", "449", "511", "577", "650", "728", "812", "902", "998", "1102", "1212", "1329", "1454", "1586", "1726", "1874", "2030", "2195", "2368", "2551", "2742", "2943", "3153", "3373", "3603", "3843", "4094", "4355", "4627", "4911", "5205", "5512", "5830", "6160", "6502", "6856", "7224", "7604", "7997", "8404", "8824", "9258", "9706", "10168", "10645", "11136" ]

[ "nonn" ]

24

0

6

[ "A011886", "A011909" ]

null

N. J. A. Sloane

2024-10-19T21:27:32

oeisdata/seq/A011/A011909.seq

48229318a86f5ee9ff7000043abfea1b

A011910

a(n) = floor( n*(n-1)*(n-2)/28 ).

[ "0", "0", "0", "0", "0", "2", "4", "7", "12", "18", "25", "35", "47", "61", "78", "97", "120", "145", "174", "207", "244", "285", "330", "379", "433", "492", "557", "626", "702", "783", "870", "963", "1062", "1169", "1282", "1402", "1530", "1665", "1807", "1958", "2117", "2284", "2460", "2644", "2838", "3040", "3252", "3474", "3706", "3948", "4200", "4462", "4735", "5019", "5315", "5621", "5940", "6270", "6612", "6966", "7332", "7712", "8104", "8509", "8928", "9360", "9805", "10265", "10739", "11227" ]

[ "nonn", "easy" ]

28

0

6

[ "A011886", "A011910" ]

null

N. J. A. Sloane

2024-10-19T21:27:48

oeisdata/seq/A011/A011910.seq

a1b8b21b8326e85c5bd040890d982b0d

A011911

a(n) = floor( n*(n-1)*(n-2)/29 ).

[ "0", "0", "0", "0", "0", "2", "4", "7", "11", "17", "24", "34", "45", "59", "75", "94", "115", "140", "168", "200", "235", "275", "318", "366", "418", "475", "537", "605", "677", "756", "840", "930", "1026", "1128", "1238", "1354", "1477", "1607", "1745", "1890", "2044", "2205", "2375", "2553", "2740", "2935", "3140", "3354", "3578", "3811", "4055", "4308", "4572", "4846", "5131", "5427", "5735", "6053", "6384", "6726", "7080", "7446", "7824", "8216", "8620", "9037", "9467", "9911", "10368", "10840" ]

[ "nonn" ]

19

0

6

[ "A011886", "A011911" ]

null

N. J. A. Sloane

2025-01-25T12:50:35

oeisdata/seq/A011/A011911.seq

f28f61dbe1d461e00b6286e349e3789e

A011912

a(n) = floor(n*(n-1)*(n-2)/30).

[ "0", "0", "0", "0", "0", "2", "4", "7", "11", "16", "24", "33", "44", "57", "72", "91", "112", "136", "163", "193", "228", "266", "308", "354", "404", "460", "520", "585", "655", "730", "812", "899", "992", "1091", "1196", "1309", "1428", "1554", "1687", "1827", "1976", "2132", "2296", "2468", "2648", "2838", "3036", "3243", "3459", "3684", "3920", "4165", "4420", "4685", "4960", "5247", "5544", "5852", "6171", "6501", "6844", "7198", "7564", "7942", "8332", "8736", "9152", "9581", "10023", "10478", "10948" ]

[ "nonn", "easy" ]

34

0

6

[ "A011886", "A011912" ]

null

N. J. A. Sloane

2024-10-19T21:36:49

oeisdata/seq/A011/A011912.seq

713542d8068c39cf534e0368b7d32f9a

A011913

a(n) = floor(n*(n - 1)*(n - 2)/31).

[ "0", "0", "0", "0", "0", "1", "3", "6", "10", "16", "23", "31", "42", "55", "70", "88", "108", "131", "157", "187", "220", "257", "298", "342", "391", "445", "503", "566", "634", "707", "785", "870", "960", "1056", "1158", "1266", "1381", "1503", "1632", "1768", "1912", "2063", "2221", "2388", "2563", "2746", "2938", "3138", "3347", "3565", "3793", "4030", "4277", "4534", "4800", "5077", "5365", "5663", "5972", "6292", "6623", "6965", "7320", "7686", "8064", "8454", "8856", "9271", "9699", "10140", "10594" ]

[ "nonn" ]

22

0

7

[ "A011886", "A011913" ]

null

N. J. A. Sloane

2024-10-19T21:40:03

oeisdata/seq/A011/A011913.seq

237cfbc41bab4f73dde7d1b0ec629eff

A011914

a(n) = floor(n*(n - 1)*(n - 2)/32).

[ "0", "0", "0", "0", "0", "1", "3", "6", "10", "15", "22", "30", "41", "53", "68", "85", "105", "127", "153", "181", "213", "249", "288", "332", "379", "431", "487", "548", "614", "685", "761", "842", "930", "1023", "1122", "1227", "1338", "1456", "1581", "1713", "1852", "1998", "2152", "2313", "2483", "2660", "2846", "3040", "3243", "3454", "3675", "3904", "4143", "4392", "4650", "4919", "5197", "5486", "5785", "6095", "6416", "6748", "7091", "7445", "7812", "8190" ]

[ "nonn", "easy" ]

26

0

7

[ "A011886", "A011914" ]

null

N. J. A. Sloane, Dec 11 1996

2024-10-21T04:34:36

oeisdata/seq/A011/A011914.seq

820c7097ee2f64246c52a345201777d9

A011915

a(n) = floor(n*(n-1)*(n-2)*(n-3)/5).

[ "0", "0", "0", "0", "4", "24", "72", "168", "336", "604", "1008", "1584", "2376", "3432", "4804", "6552", "8736", "11424", "14688", "18604", "23256", "28728", "35112", "42504", "51004", "60720", "71760", "84240", "98280", "114004", "131544", "151032", "172608", "196416", "222604", "251328", "282744", "317016", "354312" ]

[ "nonn", "easy" ]

32

0

5

[ "A000332", "A011795", "A011915", "A011917", "A011919", "A011921", "A011923", "A011924", "A011925", "A011926", "A011927", "A011928", "A011929", "A011930", "A011931", "A011932", "A011933", "A011935", "A011936", "A011937", "A011938", "A011939", "A011940", "A011941", "A011942", "A033486", "A033487", "A033488", "A034827", "A050534", "A052762", "A162668" ]

null

N. J. A. Sloane

2024-12-30T04:00:15

oeisdata/seq/A011/A011915.seq

9b4376dd6434a98133e1a50ce73ee115

A011916

a(n) = ((b(n)-1)+sqrt(3*b(n)^2-4*b(n)+1))/2, where b(n) is A011922(n).

[ "0", "3", "44", "615", "8568", "119339", "1662180", "23151183", "322454384", "4491210195", "62554488348", "871271626679", "12135248285160", "169022204365563", "2354175612832724", "32789436375292575", "456697933641263328", "6360981634602394019" ]

[ "nonn", "easy" ]

47

0

2

[ "A011916", "A011918", "A109437" ]

null

Mario Velucchi (mathchess(AT)velucchi.it)

2018-07-26T18:41:16

oeisdata/seq/A011/A011916.seq

868a6c5ba3304877791022510915654d

A011917

[ n(n-1)(n-2)(n-3)/7 ].

[ "0", "0", "0", "0", "3", "17", "51", "120", "240", "432", "720", "1131", "1697", "2451", "3432", "4680", "6240", "8160", "10491", "13289", "16611", "20520", "25080", "30360", "36432", "43371", "51257", "60171", "70200", "81432", "93960", "107880", "123291", "140297", "159003" ]

[ "nonn", "easy", "changed" ]

15

0

5

null

N. J. A. Sloane

2025-07-08T02:42:25

oeisdata/seq/A011/A011917.seq

93707e190097b03d695d055c532eebb0

A011918

a(n) = A011916(n) + A011922(n) - 1.

[ "5", "76", "1065", "14840", "206701", "2878980", "40099025", "558507376", "7779004245", "108347552060", "1509086724601", "21018866592360", "292755045568445", "4077551771365876", "56792969753553825", "791024024778387680", "11017543377143873701", "153454583255235844140", "2137346622196157944265" ]

[ "nonn", "easy" ]

28

1

[ "A011916", "A011918" ]

null

Mario Velucchi (mathchess(AT)velucchi.it)

2016-03-05T05:25:14

oeisdata/seq/A011/A011918.seq

8fcaa223669cc5af067a6eaa83d49f06

A011919

a(n) = floor(n*(n-1)*(n-2)*(n-3)/9).

[ "0", "0", "0", "0", "2", "13", "40", "93", "186", "336", "560", "880", "1320", "1906", "2669", "3640", "4853", "6346", "8160", "10336", "12920", "15960", "19506", "23613", "28336", "33733", "39866", "46800", "54600", "63336", "73080", "83906", "95893", "109120", "123669", "139626", "157080", "176120", "196840", "219336", "243706", "270053", "298480" ]

[ "nonn", "easy" ]

15

0

5

null

N. J. A. Sloane

2022-10-18T15:28:39

oeisdata/seq/A011/A011919.seq

9df3ece1c12d693902300b81a737c61f

A011920

a(n) = b(n)*(b(n)+1) = b(n) + ... + c(n), where b(n) = A011916(n), c(n) = A011918(n).

[ "12", "1980", "378840", "73419192", "14241916260", "2762844014580", "535977297450672", "103976830083273840", "20170969020163148220", "3913064012542622257452", "759114247456742016195720", "147264250942490855924510760" ]

[ "nonn", "easy" ]

19

1

null

Mario Velucchi (mathchess(AT)velucchi.it)

2024-02-07T11:55:29

oeisdata/seq/A011/A011920.seq

3f693d92f833a3d724992930c6a9c54e

A011921

[ n(n-1)(n-2)(n-3)/11 ].

[ "0", "0", "0", "0", "2", "10", "32", "76", "152", "274", "458", "720", "1080", "1560", "2184", "2978", "3970", "5192", "6676", "8456", "10570", "13058", "15960", "19320", "23184", "27600", "32618", "38290", "44672", "51820", "59792", "68650", "78458", "89280", "101184" ]

[ "nonn", "easy", "changed" ]

15

0

5

null

N. J. A. Sloane

2025-07-08T02:42:31

oeisdata/seq/A011/A011921.seq

22916ed228542b90969fcc5bed50448c

A011922

a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3) with a(0)=1, a(1)=3, and a(2)=33.

[ "1", "3", "33", "451", "6273", "87363", "1216801", "16947843", "236052993", "3287794051", "45793063713", "637815097923", "8883618307201", "123732841202883", "1723376158533153", "24003533378261251", "334326091137124353", "4656561742541479683", "64857538304443591201", "903348974519668797123", "12582028104970919568513" ]

[ "nonn", "easy", "changed" ]

90

0

2

[ "A001075", "A001353", "A007655", "A011916", "A011918", "A011920", "A011922", "A011943", "A103974" ]

null

Mario Velucchi (mathchess(AT)velucchi.it)

2025-07-10T04:32:18

oeisdata/seq/A011/A011922.seq

82a375d07870a63c0fc993881bf3a42c

A011923

[ n(n-1)(n-2)(n-3)/13 ].

[ "0", "0", "0", "0", "1", "9", "27", "64", "129", "232", "387", "609", "913", "1320", "1848", "2520", "3360", "4393", "5649", "7155", "8944", "11049", "13504", "16347", "19617", "23353", "27600", "32400", "37800", "43848", "50593", "58089", "66387", "75544", "85617", "96664" ]

[ "nonn", "easy", "changed" ]

16

0

6

null

N. J. A. Sloane

2025-07-08T02:42:36

oeisdata/seq/A011/A011923.seq

f4c79dac57d8f07786d55e8c5f08027d

A011924

Floor[n(n-1)(n-2)(n-3)/14].

[ "0", "0", "0", "0", "1", "8", "25", "60", "120", "216", "360", "565", "848", "1225", "1716", "2340", "3120", "4080", "5245", "6644", "8305", "10260", "12540", "15180", "18216", "21685", "25628", "30085", "35100", "40716", "46980", "53940", "61645", "70148", "79501", "89760" ]

[ "nonn", "easy", "changed" ]

28

0

6

null

N. J. A. Sloane

2025-07-08T02:42:43

oeisdata/seq/A011/A011924.seq

3f0d0619f86940a49d364bf44820838b

A011925

a(n) = floor(n*(n-1)*(n-2)*(n-3)/15).

[ "0", "0", "0", "0", "1", "8", "24", "56", "112", "201", "336", "528", "792", "1144", "1601", "2184", "2912", "3808", "4896", "6201", "7752", "9576", "11704", "14168", "17001", "20240", "23920", "28080", "32760", "38001", "43848", "50344", "57536", "65472", "74201", "83776" ]

[ "nonn", "easy" ]

28

0

6

null

N. J. A. Sloane

2022-09-08T08:44:37

oeisdata/seq/A011/A011925.seq

156b845c98c772931fae65e698121902

A011926

a(n) = floor(n*(n-1)*(n-2)*(n-3)/16).

[ "0", "0", "0", "0", "1", "7", "22", "52", "105", "189", "315", "495", "742", "1072", "1501", "2047", "2730", "3570", "4590", "5814", "7267", "8977", "10972", "13282", "15939", "18975", "22425", "26325", "30712", "35626", "41107", "47197", "53940", "61380", "69564", "78540" ]

[ "nonn", "easy", "changed" ]

22

0

6

null

N. J. A. Sloane

2025-07-08T02:42:48

oeisdata/seq/A011/A011926.seq

75700869a54159d746f24585f6d1f057

A011927

[ n(n-1)(n-2)(n-3)/17 ].

[ "0", "0", "0", "0", "1", "7", "21", "49", "98", "177", "296", "465", "698", "1009", "1413", "1927", "2569", "3360", "4320", "5472", "6840", "8449", "10327", "12501", "15001", "17858", "21105", "24776", "28905", "33530", "38689", "44421", "50767", "57769", "65472", "73920" ]

[ "nonn", "easy", "changed" ]

15

0

6

null

N. J. A. Sloane

2025-07-08T02:42:58

oeisdata/seq/A011/A011927.seq

22a878d18ed2a30c829a8846dd79c5a9

A011928

a(n) = floor(n(n-1)(n-2)(n-3)/18).

[ "0", "0", "0", "0", "1", "6", "20", "46", "93", "168", "280", "440", "660", "953", "1334", "1820", "2426", "3173", "4080", "5168", "6460", "7980", "9753", "11806", "14168", "16866", "19933", "23400", "27300", "31668", "36540", "41953", "47946", "54560", "61834", "69813", "78540", "88060", "98420", "109668", "121853", "135026", "149240" ]

[ "nonn", "easy" ]

16

0

6

null

N. J. A. Sloane

2022-10-18T15:28:21

oeisdata/seq/A011/A011928.seq

29f673e697e4c573654c817f59a3b75b

A011929

a(n) = floor(n(n-1)(n-2)(n-3)/19).

[ "0", "0", "0", "0", "1", "6", "18", "44", "88", "159", "265", "416", "625", "903", "1264", "1724", "2298", "3006", "3865", "4896", "6120", "7560", "9240", "11185", "13422", "15978", "18884", "22168", "25863", "30001", "34616", "39745", "45423", "51688", "58580", "66138", "74406", "83425", "93240", "103896", "115440", "127920", "141385" ]

[ "nonn", "easy" ]

16

0

6

null

N. J. A. Sloane

2022-10-18T15:29:00

oeisdata/seq/A011/A011929.seq

1ab9c5069c36ceeca5d3be524c60cad7

A011930

a(n) = floor(n(n-1)(n-2)(n-3)/20).

[ "0", "0", "0", "0", "1", "6", "18", "42", "84", "151", "252", "396", "594", "858", "1201", "1638", "2184", "2856", "3672", "4651", "5814", "7182", "8778", "10626", "12751", "15180", "17940", "21060", "24570", "28501", "32886", "37758", "43152", "49104", "55651", "62832", "70686", "79254", "88578", "98701" ]

[ "nonn", "easy" ]

28

0

6

null

N. J. A. Sloane

2023-06-13T09:04:50

oeisdata/seq/A011/A011930.seq

8225bdbf5477cff08d3a8925a7a97f5b

A011931

a(n) = floor(n*(n-1)*(n-2)*(n-3)/21).

[ "0", "0", "0", "0", "1", "5", "17", "40", "80", "144", "240", "377", "565", "817", "1144", "1560", "2080", "2720", "3497", "4429", "5537", "6840", "8360", "10120", "12144", "14457", "17085", "20057", "23400", "27144", "31320", "35960", "41097", "46765", "53001", "59840", "67320", "75480", "84360", "94001", "104445", "115737", "127920", "141040", "155144", "170280", "186497", "203845", "222377", "242144" ]

[ "nonn", "easy", "changed" ]

19

0

6

null

N. J. A. Sloane

2025-07-07T18:49:18

oeisdata/seq/A011/A011931.seq

102c53d0a40f130f2c1105471886c3f6

A011932

a(n) = floor( n*(n-1)*(n-2)*(n-3)/22 ).

[ "0", "0", "0", "0", "1", "5", "16", "38", "76", "137", "229", "360", "540", "780", "1092", "1489", "1985", "2596", "3338", "4228", "5285", "6529", "7980", "9660", "11592", "13800", "16309", "19145", "22336", "25910", "29896", "34325", "39229", "44640", "50592", "57120", "64260", "72049", "80525", "89728", "99698", "110476", "122105", "134629", "148092", "162540", "178020", "194580", "212269", "231137" ]

[ "nonn", "easy" ]

19

0

6

[ "A011915", "A011932" ]

null

N. J. A. Sloane

2024-11-03T09:33:48

oeisdata/seq/A011/A011932.seq

22e93c230e099e43fbf25525d70d8839

A011933

a(n) = floor( n*(n-1)*(n-2)*(n-3)/23 ).

[ "0", "0", "0", "0", "1", "5", "15", "36", "73", "131", "219", "344", "516", "746", "1044", "1424", "1899", "2483", "3193", "4044", "5055", "6245", "7633", "9240", "11088", "13200", "15600", "18313", "21365", "24783", "28596", "32833", "37523", "42699", "48392", "54636", "61466", "68916", "77024", "85827", "95363", "105673", "116796", "128775", "141653", "155473", "170280", "186120", "203040", "221088" ]

[ "easy", "nonn" ]

27

0

6

[ "A000332", "A011915", "A011933", "A052762" ]

null

N. J. A. Sloane

2024-11-03T09:34:05

oeisdata/seq/A011/A011933.seq

fa6ee194043cbeb7d3affcd5c02ffadb

A011934

a(n) = |1^3 - 2^3 + 3^3 - 4^3 + ... + (-1)^(n+1)*n^3|.

[ "0", "1", "7", "20", "44", "81", "135", "208", "304", "425", "575", "756", "972", "1225", "1519", "1856", "2240", "2673", "3159", "3700", "4300", "4961", "5687", "6480", "7344", "8281", "9295", "10388", "11564", "12825", "14175", "15616", "17152", "18785", "20519", "22356", "24300", "26353", "28519", "30800", "33200", "35721", "38367", "41140" ]

[ "nonn", "easy" ]

53

0

3

[ "A011934", "A015238", "A032528", "A153641" ]

null

David Penney (david(AT)math.uga.edu)

2024-11-03T09:33:53

oeisdata/seq/A011/A011934.seq

54ffee68df49d4ea8ed540d722cb77b9

A011935

a(n) = floor( n*(n-1)*(n-2)*(n-3)/25 ).

[ "0", "0", "0", "0", "0", "4", "14", "33", "67", "120", "201", "316", "475", "686", "960", "1310", "1747", "2284", "2937", "3720", "4651", "5745", "7022", "8500", "10200", "12144", "14352", "16848", "19656", "22800", "26308", "30206", "34521", "39283", "44520", "50265", "56548" ]

[ "nonn" ]

18

0

6

[ "A011915", "A011935" ]

null

N. J. A. Sloane

2025-01-18T13:46:18

oeisdata/seq/A011/A011935.seq

50991d4cd2260523a776b89875e444a2

A011936

a(n) = floor( n*(n-1)*(n-2)*(n-3)/26 ).

[ "0", "0", "0", "0", "0", "4", "13", "32", "64", "116", "193", "304", "456", "660", "924", "1260", "1680", "2196", "2824", "3577", "4472", "5524", "6752", "8173", "9808", "11676", "13800", "16200", "18900", "21924", "25296", "29044", "33193", "37772", "42808", "48332", "54373", "60964", "68136", "75924", "84360", "93480", "103320", "113916", "125308", "137533", "150632", "164644", "179612", "195577" ]

[ "nonn", "easy" ]

16

0

6

[ "A011915", "A011936" ]

null

N. J. A. Sloane

2024-10-29T03:43:53

oeisdata/seq/A011/A011936.seq

e67cc7f57bc6e62874e5e94ccdb15871

A011937

a(n) = floor( n*(n-1)*(n-2)*(n-3)/27 ).

[ "0", "0", "0", "0", "0", "4", "13", "31", "62", "112", "186", "293", "440", "635", "889", "1213", "1617", "2115", "2720", "3445", "4306", "5320", "6502", "7871", "9445", "11244", "13288", "15600", "18200", "21112", "24360", "27968", "31964", "36373", "41223", "46542", "52360", "58706", "65613", "73112", "81235", "90017", "99493", "109697", "120667", "132440", "145053", "158546", "172960", "188334" ]

[ "nonn", "easy" ]

19

0

6

[ "A011915", "A011937" ]

null

N. J. A. Sloane

2024-10-29T03:43:19

oeisdata/seq/A011/A011937.seq

6d634fb70fbb0eb1513ccedd9a6b8296

A011938

a(n) = floor( n*(n-1)*(n-2)*(n-3)/28 ).

[ "0", "0", "0", "0", "0", "4", "12", "30", "60", "108", "180", "282", "424", "612", "858", "1170", "1560", "2040", "2622", "3322", "4152", "5130", "6270", "7590", "9108", "10842", "12814", "15042", "17550", "20358", "23490", "26970", "30822", "35074", "39750", "44880", "50490", "56610", "63270", "70500", "78334", "86802", "95940", "105780" ]

[ "nonn", "easy" ]

26

0

6

[ "A011915", "A011938" ]

null

N. J. A. Sloane

2024-10-27T09:26:12

oeisdata/seq/A011/A011938.seq

679d62ac688a9d9492d8a55b2ff5f741

A011939

a(n) = floor( n*(n-1)*(n-2)*(n-3)/29 ).

[ "0", "0", "0", "0", "0", "4", "12", "28", "57", "104", "173", "273", "409", "591", "828", "1129", "1506", "1969", "2532", "3207", "4009", "4953", "6053", "7328", "8793", "10468", "12372", "14524", "16944", "19656", "22680", "26040", "29760", "33864", "38380", "43332", "48748", "54657", "61088", "68069", "75633", "83809", "92631", "102132", "112345", "123306", "135049", "147612", "161031", "175345" ]

[ "nonn", "easy" ]

20

0

6

[ "A011915", "A011939" ]

null

N. J. A. Sloane

2024-10-27T09:25:55

oeisdata/seq/A011/A011939.seq

ad410031d169d463e1c7983e4fc7f93e

A011940

a(n) = floor(n*(n-1)*(n-2)*(n-3)/30).

[ "0", "0", "0", "0", "0", "4", "12", "28", "56", "100", "168", "264", "396", "572", "800", "1092", "1456", "1904", "2448", "3100", "3876", "4788", "5852", "7084", "8500", "10120", "11960", "14040", "16380", "19000", "21924", "25172", "28768", "32736", "37100", "41888", "47124", "52836", "59052", "65800", "73112", "81016", "89544", "98728", "108600", "119196", "130548", "142692", "155664", "169500" ]

[ "nonn", "easy" ]

30

0

6

[ "A011795", "A011915", "A011940" ]

null

N. J. A. Sloane

2024-10-27T09:26:00

oeisdata/seq/A011/A011940.seq

e613ef1775475f96aaa30bcc94fbd7ac

A011941

a(n) = floor(n*(n-1)*(n-2)*(n-3)/31).

[ "0", "0", "0", "0", "0", "3", "11", "27", "54", "97", "162", "255", "383", "553", "774", "1056", "1409", "1842", "2369", "3000", "3750", "4633", "5663", "6855", "8226", "9793", "11574", "13587", "15851", "18387", "21216", "24360", "27840", "31680", "35904", "40536", "45603", "51131", "57147", "63678", "70753", "78402", "86655", "95543" ]

[ "nonn", "easy" ]

25

0

6

[ "A011915", "A011941" ]

null

N. J. A. Sloane

2024-10-27T03:13:19

oeisdata/seq/A011/A011941.seq

eddb7d297fcf0fab1c3e086d2fdd44f4

A011942

a(n) = floor( n*(n-1)*(n-2)*(n-3)/32 ).

[ "0", "0", "0", "0", "0", "3", "11", "26", "52", "94", "157", "247", "371", "536", "750", "1023", "1365", "1785", "2295", "2907", "3633", "4488", "5486", "6641", "7969", "9487", "11212", "13162", "15356", "17813", "20553", "23598", "26970", "30690", "34782", "39270", "44178", "49533", "55361", "61688", "68542", "75952", "83947", "92557", "101813", "111746", "122388", "133773", "145935", "158907", "172725" ]

[ "nonn", "easy" ]

20

0

6

[ "A011915", "A011942" ]

null

N. J. A. Sloane

2024-12-30T04:01:54

oeisdata/seq/A011/A011942.seq

d11ac7c0078f80e2d5dc390775e2fb89

A011943

Numbers k such that any group of k consecutive integers has integral standard deviation (viz. A011944(k)).

[ "1", "7", "97", "1351", "18817", "262087", "3650401", "50843527", "708158977", "9863382151", "137379191137", "1913445293767", "26650854921601", "371198523608647", "5170128475599457", "72010600134783751", "1002978273411373057", "13969685227624439047", "194572614913330773601", "2710046923559006391367" ]

[ "nonn", "easy" ]

103

1

2

[ "A000330", "A001075", "A007654", "A007655", "A011943", "A011944", "A102344", "A188644" ]

null

E. K. Lloyd

2025-02-06T08:21:05

oeisdata/seq/A011/A011943.seq

a11a3b05b83aac4c1359acd41a372cc7

A011944

a(n) = 14*a(n-1) - a(n-2) with a(0) = 0, a(1) = 2.

[ "0", "2", "28", "390", "5432", "75658", "1053780", "14677262", "204427888", "2847313170", "39657956492", "552364077718", "7693439131560", "107155783764122", "1492487533566148", "20787669686161950", "289534888072701152" ]

[ "nonn", "easy" ]

44

0

2

[ "A001353", "A007654", "A007655", "A011943", "A011944" ]

null

E. K. Lloyd

2022-06-06T08:07:59

oeisdata/seq/A011/A011944.seq

dbafb4a95d5a875acb266e713f6d51b8

A011945

Areas of almost-equilateral Heronian triangles (integral side lengths m-1, m, m+1 and integral area).

[ "0", "6", "84", "1170", "16296", "226974", "3161340", "44031786", "613283664", "8541939510", "118973869476", "1657092233154", "23080317394680", "321467351292366", "4477462600698444", "62363009058485850", "868604664218103456", "12098102289994962534", "168504827395711372020", "2346969481249964245746" ]

[ "nonn", "easy" ]

52

1

2

[ "A003500", "A007655", "A011945", "A016064", "A102341", "A103974", "A103975", "A334277", "A335025" ]

null

E. K. Lloyd

2025-02-16T08:32:32

oeisdata/seq/A011/A011945.seq

681d138eb9bea76f96413e33a35b7302

A011946

Number of Barlow packings with group P63/mmc(S) that repeat after 4n layers.

[ "1", "2", "3", "8", "15", "30", "63", "128", "252", "510", "1023", "2040", "4095", "8190", "16365", "32768", "65535", "131040", "262143", "524280", "1048509", "2097150", "4194303", "8388480", "16777200", "33554430", "67108608", "134217720", "268435455", "536870370", "1073741823", "2147483648", "4294966269", "8589934590" ]

[ "nonn", "easy" ]

43

1

2

[ "A000048", "A008683", "A011946", "A127804", "A195095" ]

null

N. J. A. Sloane

2024-04-15T07:30:33

oeisdata/seq/A011/A011946.seq

4fa0214d2eb0858924651039e4c7abc5

A011947

Number of Barlow packings with group P63/mmc(O) that repeat after 4n+2 layers.

[ "1", "1", "3", "7", "14", "31", "63", "123", "255", "511", "1015", "2047", "4092" ]

[ "nonn", "easy", "changed" ]

15

0

3

null

N. J. A. Sloane

2025-07-08T02:43:05

oeisdata/seq/A011/A011947.seq

d08dba568086a36aba5da3bcacb2e7ac

A011948

Number of Barlow packings with group P63mc that repeat after 2n layers.

[ "1", "1", "4", "7", "18", "31", "70", "126", "261", "484", "960", "1800", "3514", "6643", "12852", "24457", "47151", "90157", "173740", "333498", "643230", "1238664", "2392650", "4620006", "8939657", "17302033", "33538048", "65042495", "126289800", "245361171", "477153040", "928510506", "1808276211", "3523813566", "6871685532", "13408154100", "26178323928", "51139027135" ]

[ "nonn" ]

24

6

3

[ "A011948", "A045668", "A309784" ]

null

N. J. A. Sloane

2024-04-15T06:58:57

oeisdata/seq/A011/A011948.seq

38611693f8816e895bd385d1f74cbcce

A011949

Number of Barlow packings with group P6(bar)m2 that repeat after 2n layers.

[ "0", "0", "1", "2", "6", "12", "28", "56", "119", "240", "496", "990", "2016", "4032", "8121", "16256", "32640", "65268", "130816", "261630", "523747", "1047552", "2096128", "4192200", "8386554", "16773120", "33550216", "67100670", "134209536", "268418820", "536854528", "1073709056", "2147450383", "4294901760", "8589869022", "17179737120", "34359607296" ]

[ "nonn", "easy", "changed" ]

13

1

4

null

N. J. A. Sloane

2025-07-08T02:43:12

oeisdata/seq/A011/A011949.seq

4d21414b4baed79d5c5dbce65db7c2b8

A011950

Number of Barlow packings with group P3(bar)m1(SO) that repeat after 2n-1 layers.

[ "0", "0", "1", "3", "3", "11", "21", "39", "85", "171", "333", "683", "1364", "2715", "5461", "10923", "21813", "43687", "87381", "174699", "349525", "699051", "1397970", "2796203", "5592402", "11184555", "22369621", "44739231", "89477973", "178956971", "357913941", "715826856", "1431655743", "2863311531", "5726621013", "11453246123" ]

[ "nonn", "easy", "changed" ]

20

1

4

null

N. J. A. Sloane

2025-07-08T02:43:17

oeisdata/seq/A011/A011950.seq

2eb14d8e2b9def34a696c1ac684e2e40

A011951

Number of Barlow packings with group P3(bar)m1(S) that repeat after 2n layers.

[ "0", "0", "0", "0", "2", "3", "9", "16", "39", "75", "165", "318", "672", "1323", "2703", "5376", "10880", "21663", "43605", "87040", "174564", "348843", "698709", "1396680", "2795518", "5589675", "11183325", "22364160", "44736512", "89467320", "178951509", "357892096", "715816464", "1431612075", "2863289674", "5726534688", "11453202432" ]

[ "nonn", "easy", "changed" ]

21

1

5

null

N. J. A. Sloane

2025-07-08T02:43:24

oeisdata/seq/A011/A011951.seq

ad4da0bfc3b95bef067da5e14bcc1f0f

A011952

Number of Barlow packings with group P3(bar)m1(O) that repeat after 2n layers.

[ "2", "3", "8", "16", "40", "73", "165", "320", "666", "1323", "2709", "5364", "10880", "21675", "43577", "87040", "174590", "348787", "698709", "1396736", "2795400", "5589672", "11183445", "22363920", "44736510", "89467563", "178951005", "357892096", "715816960", "1431611083", "2863289685", "5726535661", "11453200416" ]

[ "nonn", "easy", "changed" ]

13

4

1

null

N. J. A. Sloane

2025-07-08T02:43:30

oeisdata/seq/A011/A011952.seq

d9dc0f2bcda36f1c50df75311ec70c70

A011953

Number of Barlow packings with group P3m1 that repeat after n layers.

[ "3", "2", "10", "15", "42", "68", "162", "280", "600", "1088", "2214", "4112", "8154", "15366", "30052", "57208", "111166", "212982", "412890", "794688", "1540002", "2974150", "5767344", "11167872", "21680832", "42073640", "81787057", "159005154", "309503502", "602667098" ]

[ "nonn", "easy", "changed" ]

9

1

null

N. J. A. Sloane

2025-07-08T02:43:36

oeisdata/seq/A011/A011953.seq

6c51e7a57edc1d01f3b518d14e4daf39

A011954

Barlow packings with group R3(bar)m(SO) that repeat after 6n+3 layers.

[ "1", "1", "2", "4", "11", "20", "42", "84", "170", "340", "682", "1364", "2728", "5461", "10922", "21844", "43690", "87374", "174762", "349524", "699050", "1398100", "2796192", "5592404", "11184806", "22369620", "44739242", "89478462", "178956970", "357913940", "715827882", "1431655754", "2863311486", "5726623060", "11453246122", "22906492244", "45812984490" ]

[ "nonn", "easy", "changed" ]

15

0

3

null

N. J. A. Sloane

2025-07-08T02:43:42

oeisdata/seq/A011/A011954.seq

21cee2a40e3e28989f20905c9ad14039

A011955

Number of Barlow packings with group R3(bar)m(O) that repeat after 6n layers.

[ "1", "2", "4", "9", "19", "40", "80", "165", "330", "672", "1344", "2709", "5418", "10878", "21760", "43605", "87211", "174592", "349180", "698707", "1397418", "2795520", "5591040", "11183436", "22366890", "44736512", "89473020", "178951509", "357903000", "715816960", "1431633920", "2863289683", "5726579370", "11453202383", "22906404864", "45812897109", "91625794218" ]

[ "nonn", "easy", "changed" ]

19

2

null

N. J. A. Sloane

2025-07-08T02:43:49

oeisdata/seq/A011/A011955.seq

f774e62eba40bdba3a6634943c7026e9

A011956

Number of close-packings with layer-number 3n and space group R3m.

[ "1", "2", "4", "10", "21", "42", "84", "164", "322", "620", "1200", "2300", "4429", "8482", "16303", "31259", "60105", "115472", "222332", "428106", "825774", "1593669", "3080004", "5956902", "11534689", "22352962", "43361663", "84181720", "163574114", "318079104", "619007004", "1205471654", "2349209058", "4581032192" ]

[ "nonn", "easy" ]

30

7

2

[ "A011768", "A011954", "A011955", "A011956", "A371992" ]

null

N. J. A. Sloane

2025-06-18T00:56:13

oeisdata/seq/A011/A011956.seq

f7af2159ec76bc9aaaca06cd82abd631

A011957

Number of ZnS polytypes that repeat after n layers.

[ "0", "1", "1", "1", "1", "2", "3", "6", "10", "18", "31", "59", "105", "198", "365", "688", "1285", "2438", "4599", "8755", "16647", "31806", "60787", "116570", "223696", "430290", "828514", "1598025", "3085465", "5965612", "11545611", "22370304", "43383539", "84216330", "163617801", "318148208", "619094385", "1205609454", "2349383925", "4581307186", "8939118925", "17452582356" ]

[ "nonn", "easy" ]

52

1

6

[ "A000048", "A011957", "A165920", "A165921" ]

null

N. J. A. Sloane

2019-12-05T04:21:08

oeisdata/seq/A011/A011957.seq

2a843be4e9974e9d108eb1ba563e8c91

A011958

Number of CdI_2 polytypes that repeat after 2n layers.

[ "1", "1", "3", "8", "22", "68", "216", "728", "2513", "8920", "32116", "117240", "431550", "1600734", "5970704", "22381184", "84236890", "318191804", "1205692236", "4581481776", "17452915218", "66637798834", "254960616136", "977346581800", "3753005281872" ]

[ "nonn", "easy", "changed" ]

7

1

3

null

N. J. A. Sloane

2025-07-08T02:43:55

oeisdata/seq/A011/A011958.seq

77936621c910fddbdf013687c5bf806e

A011959

Number of SiC polytypes that repeat after 2n layers.

[ "0", "0", "1", "1", "0", "1", "1", "1", "1", "3", "3", "4", "7", "11", "15", "24", "36", "55", "81", "129", "195", "301", "465", "728", "1116", "1745", "2717", "4239", "6603", "10357", "16189", "25383", "39807", "62557", "98245", "154608", "243346", "383436", "604346", "953582", "1505106", "2377442", "3757050", "5941269" ]

[ "nonn", "easy", "changed" ]

7

1

10

null

N. J. A. Sloane

2025-07-08T02:44:01

oeisdata/seq/A011/A011959.seq

2665531bf72b82afe2e478770e37d81e

A011960

Number of ferrites M_2Y_n that repeat after 6n+10 layers.

[ "0", "1", "1", "1", "1", "2", "1", "2", "2", "2", "2", "3", "2", "3", "3", "3", "3", "4", "3", "4" ]

[ "nonn", "more" ]

13

1

6

null

N. J. A. Sloane

2021-05-20T00:23:18

oeisdata/seq/A011/A011960.seq

9a439e7f2ed0caff98eaf2dbfb1785fa

A011961

Number of ferrites M_4Y_n that repeat after 6n+20 layers.

[ "0", "1", "2", "2", "3", "6", "6", "9", "13", "15", "18", "25", "27", "34", "42", "47", "54", "67", "72", "84" ]

[ "nonn", "easy", "changed" ]

7

1

3

null

N. J. A. Sloane

2025-07-08T02:44:07

oeisdata/seq/A011/A011961.seq

82245a646aa180164e411865c2791c99

A011962

Number of ferrites M_6Y_n that repeat after 6n+30 layers.

[ "0", "2", "3", "6", "9", "19", "24", "46", "62", "96", "132", "194", "249", "354", "452", "600", "762", "986", "1212", "1544" ]

[ "nonn", "easy", "changed" ]

7

1

2

null

N. J. A. Sloane

2025-07-08T02:44:13

oeisdata/seq/A011/A011962.seq

11bfd67a658037113300d49d89e9d195

A011963

Number of ferrites M_8Y_n that repeat after 6n+40 layers.

[ "0", "2", "4", "10", "19", "44", "76", "150", "251", "432", "686", "1094", "1646", "2498", "3608", "5206", "7301", "10160", "13814", "18718" ]

[ "nonn", "easy", "changed" ]

7

1

2

null

N. J. A. Sloane

2025-07-08T02:44:18

oeisdata/seq/A011/A011963.seq

379f4232508857bafedf45b7021eb999

A011964

Number of ferrites M_{10}Y_n that repeat after 6n+50 layers.

[ "0", "3", "5", "18", "38", "100", "198", "445", "829", "1605", "2851", "5014", "8361", "13843", "21907", "34362", "52327", "78571", "115434", "167695" ]

[ "nonn", "easy", "changed" ]

7

1

2

null

N. J. A. Sloane

2025-07-08T02:44:25

oeisdata/seq/A011/A011964.seq

01dd5795964858ab29899adc97e2f62b

A011965

Second differences of Bell numbers.

[ "1", "2", "7", "27", "114", "523", "2589", "13744", "77821", "467767", "2972432", "19895813", "139824045", "1028804338", "7905124379", "63287544055", "526827208698", "4551453462543", "40740750631417", "377254241891064", "3608700264369193", "35613444194346451", "362161573323083920", "3790824599495473121" ]

[ "nonn", "easy" ]

96

0

2

[ "A000110", "A005493", "A006014", "A011965", "A090365", "A106436", "A124758", "A217924", "A243499", "A284005", "A290615", "A329369", "A341392", "A347204", "A347205", "A350309" ]

null

N. J. A. Sloane

2025-01-22T11:37:47

oeisdata/seq/A011/A011965.seq

5cb1872970aab4e6ce22d96433a98263

A011966

Third differences of Bell numbers.

[ "1", "5", "20", "87", "409", "2066", "11155", "64077", "389946", "2504665", "16923381", "119928232", "888980293", "6876320041", "55382419676", "463539664643", "4024626253845", "36189297168874", "336513491259647", "3231446022478129", "32004743929977258", "326548129128737469", "3428663026172389201" ]

[ "nonn" ]

42

0

2

[ "A000110", "A005493", "A011965", "A011966", "A106436" ]

null

N. J. A. Sloane

2025-02-04T11:37:44

oeisdata/seq/A011/A011966.seq

3ba597505c7d822c863d325848f440d9

A011967

4th differences of Bell numbers.

[ "4", "15", "67", "322", "1657", "9089", "52922", "325869", "2114719", "14418716", "103004851", "769052061", "5987339748", "48506099635", "408157244967", "3561086589202", "32164670915029", "300324194090773", "2894932531218482", "28773297907499129" ]

[ "nonn" ]

23

0

1

[ "A000110", "A005493", "A011965", "A011966", "A011967", "A106436" ]

null

N. J. A. Sloane

2025-02-13T01:30:13

oeisdata/seq/A011/A011967.seq

2aed2a25f1f53205a23039f10db7fe64

A011968

Apply (1+Shift) to Bell numbers.

[ "1", "2", "3", "7", "20", "67", "255", "1080", "5017", "25287", "137122", "794545", "4892167", "31858034", "218543759", "1573857867", "11863100692", "93345011951", "764941675963", "6514819011216", "57556900440429", "526593974392123", "4981585554604074", "48658721593531669", "490110875149889635" ]

[ "nonn" ]

85

0

2

[ "A000110", "A000296", "A000569", "A011968", "A011969", "A011970", "A011971", "A106436", "A240936", "A321750" ]

null

N. J. A. Sloane

2025-02-13T01:30:09

oeisdata/seq/A011/A011968.seq

67476641b18934a10235550caaacccde

A011969

Apply (1+Shift)^2 to Bell numbers.

[ "1", "3", "5", "10", "27", "87", "322", "1335", "6097", "30304", "162409", "931667", "5686712", "36750201", "250401793", "1792401626", "13436958559", "105208112643", "858286687914", "7279760687179", "64071719451645", "584150874832552", "5508179528996197" ]

[ "nonn" ]

79

0

2

[ "A000110", "A011968", "A011969", "A011970", "A011971", "A106436" ]

null

N. J. A. Sloane

2025-04-04T01:16:42

oeisdata/seq/A011/A011969.seq

43307c591c826cdb58fec88643b3e441

A011970

Apply (1+Shift)^3 to Bell numbers.

[ "1", "4", "8", "15", "37", "114", "409", "1657", "7432", "36401", "192713", "1094076", "6618379", "42436913", "287151994", "2042803419", "15229360185", "118645071202", "963494800557", "8138047375093", "71351480138824", "648222594284197", "6092330403828749" ]

[ "nonn", "changed" ]

41

0

2

[ "A000110", "A011968", "A011969", "A011970", "A011971", "A106436" ]

null

N. J. A. Sloane

2025-07-08T02:44:31

oeisdata/seq/A011/A011970.seq

568a8fbc182ee9d28031c4a921e61e71

A011971

Aitken's array: triangle of numbers {a(n,k), n >= 0, 0 <= k <= n} read by rows, defined by a(0,0)=1, a(n,0) = a(n-1,n-1), a(n,k) = a(n,k-1) + a(n-1,k-1).

[ "1", "1", "2", "2", "3", "5", "5", "7", "10", "15", "15", "20", "27", "37", "52", "52", "67", "87", "114", "151", "203", "203", "255", "322", "409", "523", "674", "877", "877", "1080", "1335", "1657", "2066", "2589", "3263", "4140", "4140", "5017", "6097", "7432", "9089", "11155", "13744", "17007", "21147", "21147", "25287", "30304", "36401", "43833", "52922", "64077", "77821", "94828", "115975" ]

[ "tabl", "nonn", "easy", "nice" ]

132

0

3

[ "A000110", "A005493", "A011965", "A011966", "A011968", "A011969", "A011971", "A011972", "A046934", "A094577", "A095149", "A106436", "A108041", "A108042", "A108043", "A123346" ]

null

N. J. A. Sloane, J. H. Conway and R. K. Guy

2025-02-16T08:32:32

oeisdata/seq/A011/A011971.seq

63ecc87aa7951aa78c66a929cbfc5ef6

A011972

Sequence formed by reading rows of triangle defined in A011971.

[ "1", "2", "3", "5", "7", "10", "15", "20", "27", "37", "52", "67", "87", "114", "151", "203", "255", "322", "409", "523", "674", "877", "1080", "1335", "1657", "2066", "2589", "3263", "4140", "5017", "6097", "7432", "9089", "11155", "13744", "17007", "21147", "25287", "30304", "36401", "43833", "52922", "64077", "77821", "94828" ]

[ "nonn", "easy", "tabl" ]

30

0

2

null

N. J. A. Sloane and J. H. Conway

2023-12-02T05:09:49

oeisdata/seq/A011/A011972.seq

1fc9dc186adebfb754241a1c4be241cf

A011973

Irregular triangle read by rows: T(n,k) = binomial(n-k, k), n >= 0, 0 <= k <= floor(n/2); or, coefficients of (one version of) Fibonacci polynomials.

[ "1", "1", "1", "1", "1", "2", "1", "3", "1", "1", "4", "3", "1", "5", "6", "1", "1", "6", "10", "4", "1", "7", "15", "10", "1", "1", "8", "21", "20", "5", "1", "9", "28", "35", "15", "1", "1", "10", "36", "56", "35", "6", "1", "11", "45", "84", "70", "21", "1", "1", "12", "55", "120", "126", "56", "7", "1", "13", "66", "165", "210", "126", "28", "1", "1", "14", "78", "220", "330", "252", "84", "8", "1", "15", "91", "286", "495", "462" ]

[ "tabf", "easy", "nonn", "nice" ]

337

0

6

[ "A000045", "A000108", "A000129", "A000930", "A007318", "A011973", "A025581", "A030528", "A049310", "A052553", "A053122", "A053123", "A054123", "A054142", "A055087", "A055151", "A092865", "A098474", "A098925", "A102426", "A124644", "A134264", "A169803", "A332602" ]

null

N. J. A. Sloane

2025-02-16T08:32:32

oeisdata/seq/A011/A011973.seq

5bd6453daf9116ce4e1d49e8cbbc0f5a

A011974

2 followed by the numbers that are the sum of 2 successive primes.

[ "2", "5", "8", "12", "18", "24", "30", "36", "42", "52", "60", "68", "78", "84", "90", "100", "112", "120", "128", "138", "144", "152", "162", "172", "186", "198", "204", "210", "216", "222", "240", "258", "268", "276", "288", "300", "308", "320", "330", "340", "352", "360", "372", "384", "390", "396", "410", "434", "450", "456", "462", "472", "480", "492", "508", "520" ]

[ "nonn", "easy" ]

22

1

[ "A000040", "A011974" ]

null

N. J. A. Sloane

2022-06-25T12:53:39

oeisdata/seq/A011/A011974.seq

83f043d2db2300e48f04794bb26931e7

A011975

Covering numbers C(n,3,2).

[ "1", "3", "4", "6", "7", "11", "12", "17", "19", "24", "26", "33", "35", "43", "46", "54", "57", "67", "70", "81", "85", "96", "100", "113", "117", "131", "136", "150", "155", "171", "176", "193", "199", "216", "222", "241", "247", "267", "274", "294", "301", "323", "330", "353", "361", "384", "392", "417", "425", "451", "460", "486" ]

[ "nonn", "easy" ]

32

3

2

[ "A001839", "A011975", "A011976", "A011977", "A036838", "A066010" ]

null

N. J. A. Sloane

2024-01-10T20:13:00

oeisdata/seq/A011/A011975.seq

6ce98c7ced0f8fab47627e3ad782bf1b

A011976

Covering numbers C(n,4,2).

[ "1", "3", "3", "5", "6", "8", "9", "11", "12", "13", "18", "19", "20", "26", "27", "31", "35", "37", "39", "46", "48", "50", "59", "61", "63", "73", "75", "78", "88", "91", "94", "105", "108", "111", "124", "127", "130", "144", "147", "151", "165", "169", "173", "188", "192", "196", "213", "217", "221", "239", "243", "248", "266", "271", "276", "295", "300", "305", "326" ]

[ "nonn", "easy", "changed" ]

16

4

2

[ "A011975", "A011976", "A011977" ]

null

N. J. A. Sloane

2025-07-08T02:44:39

oeisdata/seq/A011/A011976.seq

198740203f6b65cc97c73ecd51d7a871

A011977

Covering numbers C(n,5,2).

[ "1", "3", "3", "4", "5", "6", "7", "9", "10", "12", "13", "15", "16", "18", "19", "21", "21", "27", "28", "30", "30", "37", "38", "40" ]

[ "nonn", "hard", "changed" ]

16

5

2

[ "A011975", "A011977", "A240116" ]

null

N. J. A. Sloane

2025-07-08T02:44:47

oeisdata/seq/A011/A011977.seq

7f68d8ddb0c7b0f2db8adc405eeff43d

A011978

Covering numbers C(n,6,2).

[ "1", "3", "3", "3", "4", "6", "6", "7", "7", "10", "10", "12", "12", "15", "16", "17", "19" ]

[ "nonn", "hard", "more" ]

12

6

2

null

N. J. A. Sloane

2023-09-21T16:57:32

oeisdata/seq/A011/A011978.seq

40c1f2f9a8e79520f03e3dbc51c0e7a6

A011979

Covering numbers C(n,4,3) (next term is <= 261).

[ "1", "4", "6", "12", "14", "25", "30", "47", "57", "78", "91", "124", "140", "183", "207" ]

[ "nonn", "hard" ]

13

4

2

[ "A011979", "A066010" ]

null

N. J. A. Sloane

2020-02-02T21:33:55

oeisdata/seq/A011/A011979.seq

3c95faeb745c71363030096e5c0f6f83

A011980

Covering numbers C(n,5,3) (next term is <= 29).

[ "1", "4", "5", "8", "12", "17", "20" ]

[ "nonn", "hard", "changed" ]

11

5

2

null

N. J. A. Sloane

2025-07-08T02:44:53

oeisdata/seq/A011/A011980.seq

5ba2a857b1cc3b8da336934c9f3eed48

A011981

Covering numbers C(n,6,3) (next term is <= 21).

[ "1", "4", "4", "7", "10", "11", "15" ]

[ "nonn", "hard", "changed" ]

11

6

2

null

N. J. A. Sloane

2025-07-08T02:45:00

oeisdata/seq/A011/A011981.seq

545bb67ee421b96614a110f57770bcae

A011982

Covering numbers C(n,7,3) (next term is <= 25).

[ "1", "4", "4", "6", "8", "11", "13", "14", "15" ]

[ "nonn", "hard", "changed" ]

11

7

2

null

N. J. A. Sloane

2025-07-08T02:45:06

oeisdata/seq/A011/A011982.seq

daf2ed0b8989ffd5f368c0ffc9a9ce51

A011983

Covering numbers C(n,5,4).

[ "1", "5", "9", "20", "30", "51", "66", "113" ]

[ "nonn", "hard" ]

19

5

2

[ "A011983", "A066009", "A066010" ]

null

N. J. A. Sloane

2023-08-24T13:42:22

oeisdata/seq/A011/A011983.seq

23164c31451b69d2380e9c05f0442e3e

A011984

Covering numbers C(n,6,4) (next term is <= 41).

[ "5", "7", "12", "20", "32" ]

[ "nonn", "more", "hard", "changed" ]

15

6

1

null

N. J. A. Sloane

2025-07-08T02:45:12

oeisdata/seq/A011/A011984.seq

0b230700b8f3cebb17c27fc49c9fde81

A011985

Covering numbers C(n,7,4) (next term is <= 24).

[ "1", "5", "6", "10", "17" ]

[ "nonn", "hard", "changed" ]

11

7

2

null

N. J. A. Sloane

2025-07-08T02:45:19

oeisdata/seq/A011/A011985.seq

7bfe27de9b36e0bc01ccff36b8e8d57d

A011986

Covering numbers C(n,7,4) (next term is <= 19).

[ "1", "5", "5", "9", "12" ]

[ "nonn", "hard", "changed" ]

11

8

2

null

N. J. A. Sloane

2025-07-08T02:45:25

oeisdata/seq/A011/A011986.seq

5656ed38ed9ef0e450da58ca33db7a0b

A011987

Covering numbers C(n,6,5) (next term is <= 100).

[ "1", "6", "12", "30", "50" ]

[ "nonn", "hard" ]

13

6

2

[ "A011987", "A066010" ]

null

N. J. A. Sloane

2020-02-02T21:33:25

oeisdata/seq/A011/A011987.seq

442ffcb7e0a3611923ebb6576eaa2304

A011988

Covering numbers C(n,7,5) (next term is <= 34).

[ "1", "6", "9", "20" ]

[ "nonn", "hard", "changed" ]

11

7

2

null

N. J. A. Sloane

2025-07-08T02:45:31

oeisdata/seq/A011/A011988.seq

16aeba958eb8229fa41ec58e90acc669

A011989

Covering numbers C(n,8,5) (next term is <= 43).

[ "1", "6", "8", "16", "26" ]

[ "nonn", "hard", "changed" ]

11

8

2

null

N. J. A. Sloane

2025-07-08T02:45:39

oeisdata/seq/A011/A011989.seq

0eddcbfe6d65e95c2001bf10d028dd74

A011990

Covering numbers C(n,9,5) (next term is <= 19).

[ "1", "6", "7", "12" ]

[ "nonn", "hard" ]

12

9

2

null

N. J. A. Sloane

2019-12-30T15:08:51

oeisdata/seq/A011/A011990.seq

589db526c7f337598af5a23e6cd88b56

A011991

(n,3,1) difference families over Z_n.

[ "1", "0", "0", "0", "0", "0", "1", "0", "2", "0", "0", "0", "4", "0", "7", "0", "0", "0", "12", "0", "8", "0", "0", "0", "80", "0", "84", "0", "0", "0", "820", "0", "798", "0", "0", "0", "9508", "0", "11616", "0", "0", "0", "157340", "0", "139828", "0", "0", "0", "3027456", "0", "2353310" ]

[ "nonn", "changed" ]

6

7

9

null

N. J. A. Sloane

2025-07-08T02:45:44

oeisdata/seq/A011/A011991.seq

056b61516b2f5079527c02aba0aed2b2

A011992

(n,3,2) difference families over Z_n.

[ "2", "0", "0", "0", "0", "4", "9", "0", "9", "71", "0", "0", "201", "0", "175", "0", "0", "2939", "19543", "0", "10841", "609483" ]

[ "nonn", "hard", "changed" ]

6

7

1

null

N. J. A. Sloane

2025-07-08T02:46:04

oeisdata/seq/A011/A011992.seq

4f3809dec28ab1cc473d7d2d08e0fa41

A011993

(2n+1,3,3) difference families over Z_{2n+1}.

[ "1", "3", "4", "8", "47", "421", "1550", "13316", "212968" ]

[ "nonn", "hard", "changed" ]

6

2

null

N. J. A. Sloane

2025-07-08T02:46:10

oeisdata/seq/A011/A011993.seq

f9dcaa8431149e4c357d795cfecbf358

A011994

(n,3,4) difference families over Z_n.

[ "2", "4", "0", "3", "21", "0", "180", "253", "0", "2981", "21742", "0", "320760" ]

[ "nonn", "hard", "changed" ]

6

1

null

N. J. A. Sloane

2025-07-08T02:46:17

oeisdata/seq/A011/A011994.seq

9e4356a08f97f26d2fa275ed594dd2a9

A011995

(n,3,5) difference families over Z_n.

[ "5", "0", "4", "0", "0", "0", "1224", "0", "15686", "0", "0", "0" ]

[ "nonn", "hard", "changed" ]

6

7

1

null

N. J. A. Sloane

2025-07-08T02:46:22

oeisdata/seq/A011/A011995.seq

786d929e5491d8be3103054df4109970

A011996

(n,3,6) difference families over Z_n.

[ "1", "0", "7", "12", "24", "0", "209", "3561", "5285", "0", "375372", "2460490" ]

[ "nonn", "hard", "changed" ]

6

5

3

null

N. J. A. Sloane

2025-07-08T02:46:29

oeisdata/seq/A011/A011996.seq

eb579b9157e774997cf403fa9f889491

A011997

Number of (n,3,7) difference families over Z_n.

[ "8", "0", "27", "0", "0", "0", "20347", "0" ]

[ "nonn", "hard", "changed" ]

7

1

null

N. J. A. Sloane

2025-07-08T02:46:35

oeisdata/seq/A011/A011997.seq

37765a9a747e89c60aff2d32eb936d80

A011998

(n,3,8) difference families over Z_n.

[ "3", "10", "0", "30", "360", "0", "15264", "70924", "0" ]

[ "nonn", "hard", "changed" ]

6

1

null

N. J. A. Sloane

2025-07-08T02:46:41

oeisdata/seq/A011/A011998.seq

3b068b52398568106dc0ee98487e48c8

A011999

(2n+1,3,9) difference families over Z_{2n+1}.

[ "1", "12", "108", "2593", "225900" ]

[ "nonn", "hard", "changed" ]

6

2

null

N. J. A. Sloane

2025-07-08T02:46:47

oeisdata/seq/A011/A011999.seq

9ac8525cc52bb15ff0399d1074eb723b

A012000

Expansion of 1/sqrt(1 - 4*x + 16*x^2).

[ "1", "2", "-2", "-28", "-74", "92", "1324", "3656", "-4826", "-70228", "-197372", "267896", "3921724", "11126936", "-15347432", "-225505648", "-643622906", "897078476", "13214495764", "37869162392", "-53170602284", "-784672445368", "-2255295815192", "3183829452272", "47051201187676", "135537088268792", "-192142210448216" ]

[ "sign" ]

68

0

2

[ "A012000", "A098332", "A116091", "A126869" ]

null

Wouter Meeussen

2021-12-04T12:25:07

oeisdata/seq/A012/A012000.seq

0ab012f66018817a82aef290ad04008f