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2025-04-28 00:58:08
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A008901 | x->x/2 if x even, x->3x-1 if x odd. | [
"90",
"45",
"134",
"67",
"200",
"100",
"50",
"25",
"74",
"37",
"110",
"55",
"164",
"82",
"41",
"122",
"61",
"182",
"91",
"272",
"136",
"68",
"34",
"17",
"50",
"25",
"74",
"37",
"110",
"55",
"164",
"82",
"41",
"122",
"61",
"182",
"91",
"272",
"136",
"68",
"34",
"17",
"50",
"25",
"74",
"37",
"110",
"55",
"164"
]
| [
"nonn"
]
| 6 | 0 | 1 | null | null | N. J. A. Sloane. | 2016-12-08T12:22:14 | oeisdata/seq/A008/A008901.seq | 3027387d432f8ba86cc8825f5dab0bc5 |
A008902 | x->x/2 if x even, x->3x-1 if x odd. | [
"99",
"296",
"148",
"74",
"37",
"110",
"55",
"164",
"82",
"41",
"122",
"61",
"182",
"91",
"272",
"136",
"68",
"34",
"17",
"50",
"25",
"74",
"37",
"110",
"55",
"164",
"82",
"41",
"122",
"61",
"182",
"91",
"272",
"136",
"68",
"34",
"17",
"50",
"25",
"74",
"37",
"110",
"55",
"164",
"82",
"41",
"122",
"61",
"182",
"91"
]
| [
"nonn"
]
| 6 | 0 | 1 | null | null | N. J. A. Sloane. | 2016-12-08T12:23:21 | oeisdata/seq/A008/A008902.seq | f3ff674d1f55bd52db065c16885617bc |
A008903 | x->x/2 if x even, x->3x-1 if x odd. | [
"100",
"50",
"25",
"74",
"37",
"110",
"55",
"164",
"82",
"41",
"122",
"61",
"182",
"91",
"272",
"136",
"68",
"34",
"17",
"50",
"25",
"74",
"37",
"110",
"55",
"164",
"82",
"41",
"122",
"61",
"182",
"91",
"272",
"136",
"68",
"34",
"17",
"50",
"25",
"74",
"37",
"110",
"55",
"164",
"82",
"41",
"122",
"61",
"182",
"91"
]
| [
"nonn"
]
| 10 | 0 | 1 | null | null | N. J. A. Sloane. | 2021-05-20T17:03:53 | oeisdata/seq/A008/A008903.seq | 20db9070fc4664eed1d8f17ab18e8268 |
A008904 | a(n) is the final nonzero digit of n!. | [
"1",
"1",
"2",
"6",
"4",
"2",
"2",
"4",
"2",
"8",
"8",
"8",
"6",
"8",
"2",
"8",
"8",
"6",
"8",
"2",
"4",
"4",
"8",
"4",
"6",
"4",
"4",
"8",
"4",
"6",
"8",
"8",
"6",
"8",
"2",
"2",
"2",
"4",
"2",
"8",
"2",
"2",
"4",
"2",
"8",
"6",
"6",
"2",
"6",
"4",
"2",
"2",
"4",
"2",
"8",
"4",
"4",
"8",
"4",
"6",
"6",
"6",
"2",
"6",
"4",
"6",
"6",
"2",
"6",
"4",
"8",
"8",
"6",
"8",
"2",
"4",
"4",
"8",
"4",
"6",
"8",
"8",
"6",
"8",
"2",
"2",
"2",
"4",
"2",
"8",
"2",
"2",
"4",
"2",
"8",
"6",
"6",
"2",
"6"
]
| [
"nonn",
"base",
"nice"
]
| 174 | 0 | 3 | [
"A000142",
"A004154",
"A008904",
"A008905",
"A034886",
"A045547",
"A045548",
"A045549",
"A045550",
"A136690",
"A136691",
"A136692",
"A136693",
"A136694",
"A136695",
"A136696",
"A136697",
"A136698",
"A136699",
"A136700",
"A136701",
"A136702"
]
| null | Russ Cox | 2025-04-03T08:59:42 | oeisdata/seq/A008/A008904.seq | a21e9dc085ffc4ce76dbca0c99f52bd9 |
A008905 | Leading digit of n!. | [
"1",
"1",
"2",
"6",
"2",
"1",
"7",
"5",
"4",
"3",
"3",
"3",
"4",
"6",
"8",
"1",
"2",
"3",
"6",
"1",
"2",
"5",
"1",
"2",
"6",
"1",
"4",
"1",
"3",
"8",
"2",
"8",
"2",
"8",
"2",
"1",
"3",
"1",
"5",
"2",
"8",
"3",
"1",
"6",
"2",
"1",
"5",
"2",
"1",
"6",
"3",
"1",
"8",
"4",
"2",
"1",
"7",
"4",
"2",
"1",
"8",
"5",
"3",
"1",
"1",
"8",
"5",
"3",
"2",
"1",
"1",
"8",
"6",
"4",
"3",
"2",
"1",
"1",
"1",
"8",
"7",
"5",
"4",
"3",
"3",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"1"
]
| [
"nonn",
"base",
"easy"
]
| 59 | 0 | 3 | [
"A000142",
"A000966",
"A008905",
"A018799",
"A202021",
"A213201"
]
| null | Russ Cox | 2025-01-05T19:51:34 | oeisdata/seq/A008/A008905.seq | 75137c93a1e05416217e754c46c10940 |
A008906 | Number of digits in n! excluding final zeros. | [
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"3",
"4",
"5",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"15",
"15",
"16",
"18",
"19",
"20",
"20",
"21",
"23",
"24",
"25",
"26",
"27",
"29",
"30",
"32",
"33",
"34",
"36",
"37",
"39",
"39",
"41",
"43",
"44",
"46",
"47",
"48",
"50",
"52",
"53",
"53",
"55",
"56",
"58",
"60",
"61",
"62",
"64",
"66",
"68",
"68",
"70",
"72",
"74",
"76",
"76",
"78",
"80",
"82",
"84",
"85",
"86",
"88",
"90",
"92",
"92",
"94"
]
| [
"nonn",
"base",
"easy"
]
| 30 | 0 | 5 | [
"A008906",
"A027868",
"A034886"
]
| null | Russ Cox | 2021-11-21T07:34:55 | oeisdata/seq/A008/A008906.seq | b6bcf5a453205ed188723546db29cc5e |
A008907 | Number of legal tic-tac-toe (or noughts and crosses) positions after n plays, up to rotation and reflection. | [
"1",
"3",
"12",
"38",
"108",
"174",
"204",
"153",
"57",
"15"
]
| [
"nonn",
"fini",
"full"
]
| 16 | 0 | 2 | null | null | Russ Cox | 2012-03-30T18:35:06 | oeisdata/seq/A008/A008907.seq | e458e46faaf781cacde4459a7c51207e |
A008908 | a(n) = (1 + number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem), or -1 if 1 is never reached. | [
"1",
"2",
"8",
"3",
"6",
"9",
"17",
"4",
"20",
"7",
"15",
"10",
"10",
"18",
"18",
"5",
"13",
"21",
"21",
"8",
"8",
"16",
"16",
"11",
"24",
"11",
"112",
"19",
"19",
"19",
"107",
"6",
"27",
"14",
"14",
"22",
"22",
"22",
"35",
"9",
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"9",
"30",
"17",
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"17",
"105",
"12",
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"113",
"113",
"20",
"33",
"20",
"33",
"20",
"20",
"108",
"108",
"7",
"28",
"28",
"28",
"15",
"15",
"15",
"103"
]
| [
"nonn",
"nice",
"look"
]
| 70 | 1 | 2 | [
"A006370",
"A006577",
"A006667",
"A008908",
"A075677"
]
| null | N. J. A. Sloane, Bill Gosper | 2024-07-22T08:27:51 | oeisdata/seq/A008/A008908.seq | 367573434f98a446e12704a52935d269 |
A008909 | Join 2n points on a line with n arcs above the line; form graph with the arcs as nodes, joining 2 nodes when the arcs cross. a(n) is the number of cases in which the graph is a path. | [
"1",
"1",
"3",
"8",
"21",
"56",
"153",
"428",
"1222",
"3549",
"10454",
"31159",
"93801",
"284788",
"871007",
"2681018",
"8298932",
"25817395",
"80674901",
"253106836",
"796968055",
"2517706036",
"7977573202",
"25347126629",
"80738862084",
"257778971503",
"824798533932",
"2644335308021",
"8493626448823"
]
| [
"nonn"
]
| 29 | 1 | 3 | null | null | Martin Klazar | 2019-12-18T09:09:18 | oeisdata/seq/A008/A008909.seq | 85208f8d3d25d7bd3cf65b329bc31ade |
A008910 | Join 2n points on a line with n arcs above the line; form graph with the arcs as nodes, joining 2 nodes when the arcs cross. a(n) is the number of cases in which the graph is symmetric about middle and has no isolated nodes. | [
"0",
"1",
"2",
"9",
"26",
"122",
"466",
"2299",
"10316",
"54179"
]
| [
"nonn"
]
| 5 | 1 | 3 | null | null | klazar(AT)kam.mff.cuni.cz (Martin Klazar) | 2003-05-16T03:00:00 | oeisdata/seq/A008/A008910.seq | 0c6e06debfeea4485b777fd89f87e5d3 |
A008911 | a(n) = n^2*(n^2 - 1)/6. | [
"0",
"0",
"2",
"12",
"40",
"100",
"210",
"392",
"672",
"1080",
"1650",
"2420",
"3432",
"4732",
"6370",
"8400",
"10880",
"13872",
"17442",
"21660",
"26600",
"32340",
"38962",
"46552",
"55200",
"65000",
"76050",
"88452",
"102312",
"117740",
"134850",
"153760",
"174592",
"197472",
"222530",
"249900",
"279720",
"312132"
]
| [
"nonn",
"easy"
]
| 83 | 0 | 3 | [
"A002378",
"A002415",
"A005408",
"A006011",
"A008911",
"A033488",
"A047928",
"A083374"
]
| null | N. J. A. Sloane, R. K. Guy | 2024-01-20T17:55:40 | oeisdata/seq/A008/A008911.seq | b8eda97990e745fd8a18348c2b1f7952 |
A008912 | Truncated triangular numbers (of form n*(n-3)/2 - k^2+k*n+1 for 1<=k<n). | [
"1",
"3",
"6",
"7",
"10",
"12",
"15",
"18",
"19",
"21",
"25",
"27",
"28",
"33",
"36",
"37",
"42",
"45",
"46",
"48",
"52",
"55",
"57",
"60",
"61",
"63",
"66",
"69",
"73",
"75",
"78",
"82",
"87",
"88",
"90",
"91",
"96",
"102",
"105",
"106",
"108",
"111",
"117",
"118",
"120",
"123",
"126",
"127",
"133",
"135",
"136",
"141",
"144",
"145",
"147",
"150",
"153",
"160",
"162",
"165"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A008867",
"A008912"
]
| null | N. J. A. Sloane, R. K. Guy | 2018-11-14T15:49:52 | oeisdata/seq/A008/A008912.seq | 2f9f07cc117e6d36ad1fd51bd5143188 |
A008913 | Order of simple Chevalley group F_4(q), q = prime power. | [
"3311126603366400",
"5734420792816671844761600",
"19009825523840945451297669120000",
"2131486317725501953125000000000000000",
"86325573304608766361629193317905069834240000"
]
| [
"nonn",
"easy"
]
| 15 | 1 | 1 | [
"A008913",
"A178779"
]
| null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008913.seq | 50444796b3d1867b0c13f2c6f5152c29 |
A008914 | Order of simple Chevalley group G_2 (q), q = prime power. | [
"12096",
"4245696",
"251596800",
"5859000000",
"664376138496",
"4329310519296",
"22594320403200",
"376611192619200",
"3914077489672896",
"71776114783027200",
"167795197370551296",
"796793353927300800",
"11570921621943780096"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A008914",
"A037248"
]
| null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008914.seq | 80a0e570804371845ae906fe9ccab9bf |
A008915 | Order of universal twisted Chevalley group 2_E_6 (q), q = prime power. | [
"229597439051324561817600",
"14636855916969695633965120680532377600",
"85696576147617709485896772387584983695360000000",
"3177180118884729605172792434692382812500000000000000000"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A008915",
"A178798"
]
| null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008915.seq | b16925eb70cd4ed0ebc9137a04262aed |
A008916 | Order of simple twisted Chevalley group 2_E_6 (q), q = prime power. | [
"76532479683774853939200",
"14636855916969695633965120680532377600",
"85696576147617709485896772387584983695360000000",
"1059060039628243201724264144897460937500000000000000000"
]
| [
"nonn"
]
| 9 | 1 | 1 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008916.seq | b558cf55a011c3f90fdc34f9cda62a0c |
A008917 | Numbers that are the sum of 3 positive cubes in more than one way. | [
"251",
"1009",
"1366",
"1457",
"1459",
"1520",
"1730",
"1737",
"1756",
"1763",
"1793",
"1854",
"1945",
"2008",
"2072",
"2241",
"2414",
"2456",
"2458",
"2729",
"2736",
"3060",
"3391",
"3457",
"3592",
"3599",
"3655",
"3745",
"3926",
"4105",
"4112",
"4131",
"4168",
"4229",
"4320",
"4376",
"4402",
"4437",
"4447"
]
| [
"nonn",
"easy",
"nice"
]
| 40 | 1 | 1 | [
"A001235",
"A003072",
"A008917",
"A024796",
"A025396",
"A025398",
"A025406",
"A309762"
]
| null | N. J. A. Sloane and J. H. Conway | 2021-08-05T15:28:50 | oeisdata/seq/A008/A008917.seq | 2ae6a076594618276bef3a5637e13892 |
A008918 | Numbers k such that 4*k = (k written backwards), k > 0. | [
"2178",
"21978",
"219978",
"2199978",
"21782178",
"21999978",
"217802178",
"219999978",
"2178002178",
"2197821978",
"2199999978",
"21780002178",
"21978021978",
"21999999978",
"217800002178",
"217821782178",
"219780021978",
"219978219978",
"219999999978",
"2178000002178",
"2178219782178"
]
| [
"nonn",
"base"
]
| 50 | 1 | 1 | [
"A001232",
"A008918",
"A008919",
"A031877",
"A193434",
"A222814",
"A222815"
]
| null | N. J. A. Sloane | 2025-01-09T10:13:05 | oeisdata/seq/A008/A008918.seq | 46372978a43a03d550cc426a0052a7e2 |
A008919 | Numbers k such that k written backwards is a nontrivial multiple of k. | [
"1089",
"2178",
"10989",
"21978",
"109989",
"219978",
"1099989",
"2199978",
"10891089",
"10999989",
"21782178",
"21999978",
"108901089",
"109999989",
"217802178",
"219999978",
"1089001089",
"1098910989",
"1099999989",
"2178002178",
"2197821978",
"2199999978",
"10890001089"
]
| [
"nonn",
"base",
"nice"
]
| 116 | 1 | 1 | [
"A001232",
"A004086",
"A008918",
"A008919",
"A031877",
"A103609",
"A214927"
]
| null | N. J. A. Sloane | 2025-02-22T10:43:14 | oeisdata/seq/A008/A008919.seq | 4f565f3e3d7b9ec848b09e211c865402 |
A008920 | Let j = | i - i_written_backwards |, k = j + j_written_backwards; then k is in this sequence. | [
"0",
"18",
"99",
"198",
"261",
"342",
"423",
"504",
"585",
"666",
"747",
"828",
"909",
"1089",
"1170",
"1251",
"1332",
"1413",
"1494",
"1575",
"1656",
"1737",
"1818",
"1881",
"1998",
"2772",
"2871",
"3663",
"3762",
"4554",
"4653",
"5445",
"5544",
"6336",
"6435",
"7227",
"7326",
"8118",
"8217",
"9009",
"9108",
"9999",
"10890",
"10989",
"11781"
]
| [
"nonn",
"base"
]
| 30 | 1 | 2 | [
"A004086",
"A008920",
"A335978"
]
| null | N. J. A. Sloane and J. H. Conway | 2021-11-20T21:27:18 | oeisdata/seq/A008/A008920.seq | 51d185fb08bf7387eef9029f8c6a7cda |
A008921 | Coordination sequence for lattice {E_7}*. | [
"1",
"56",
"938",
"7688",
"39746",
"150248",
"455114",
"1171928",
"2668610",
"5521880",
"10585514",
"19068392",
"32622338",
"53439752",
"84361034",
"128991800",
"191829890",
"278402168",
"395411114",
"550891208",
"754375106",
"1017069608",
"1352041418",
"1774412696",
"2301566402",
"2953361432",
"3752357546",
"4724050088",
"5897114498"
]
| [
"nonn"
]
| 18 | 0 | 2 | null | null | N. J. A. Sloane | 2022-09-08T08:44:36 | oeisdata/seq/A008/A008921.seq | f630c8e0154a21b7de2a24694ade3db6 |
A008922 | Crystal ball sequence for lattice {E_7}*. | [
"1",
"57",
"995",
"8683",
"48429",
"198677",
"653791",
"1825719",
"4494329",
"10016209",
"20601723",
"39670115",
"72292453",
"125732205",
"210093239",
"339085039",
"530914929",
"809317097",
"1204728211",
"1755619419",
"2509994525",
"3527064133",
"4879105551",
"6653518247",
"8955084649",
"11908446081",
"15660803627",
"20384853715"
]
| [
"nonn",
"nice",
"easy"
]
| 25 | 0 | 2 | null | null | N. J. A. Sloane | 2022-09-08T08:44:36 | oeisdata/seq/A008/A008922.seq | 0602dde80db0089fa81e9d6dfed614d9 |
A008923 | Euler's family of solutions to n = x^4 + y^4 = z^4 + w^4. | [
"90239171293339457",
"43217672330080936976",
"6822171645549542113537",
"497455247066570553051152",
"20549128177340906621890817",
"24223393095189686902587392",
"549140647573975773898200592"
]
| [
"nonn"
]
| 6 | 1 | 1 | [
"A003824",
"A008923"
]
| null | N. J. A. Sloane. | 2012-03-30T16:45:26 | oeisdata/seq/A008/A008923.seq | dfbc4d3d5215594c1e57ee55866967dd |
A008924 | Harmonic Molien series for Conway group Con.0. | [
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"3",
"1",
"3",
"4",
"5",
"5",
"10",
"8",
"14",
"17",
"22",
"27",
"44",
"45",
"69",
"90",
"123",
"157",
"240",
"299",
"445",
"610",
"884",
"1237",
"1871",
"2635",
"3975",
"5823",
"8751",
"12918",
"19570",
"28977",
"43644",
"64880",
"96983",
"143510",
"213118"
]
| [
"nonn",
"more"
]
| 15 | 0 | 13 | [
"A008924",
"A008925"
]
| null | N. J. A. Sloane and J. H. Conway, Aug 14 1977 | 2022-12-29T06:24:26 | oeisdata/seq/A008/A008924.seq | 1cf2973e6773390c014ff5d208ff5b4d |
A008925 | Molien series for Conway group Con.0. | [
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"3",
"4",
"5",
"6",
"9",
"10",
"13",
"17",
"22",
"27",
"37",
"45",
"59",
"76",
"98",
"125",
"169",
"214",
"283",
"373",
"496",
"653",
"893",
"1192",
"1637",
"2247",
"3131",
"4368",
"6239",
"8874",
"12849",
"18672",
"27423",
"40341",
"59911",
"88888",
"132532",
"197412"
]
| [
"nonn",
"more"
]
| 13 | 0 | 7 | [
"A008924",
"A008925"
]
| null | N. J. A. Sloane and J. H. Conway, Aug 14 1977 | 2022-12-29T06:24:19 | oeisdata/seq/A008/A008925.seq | 6886a05ca14a4ecfcdd0764aaf8c2d0b |
A008926 | Number of uniquely agreeing sequences. | [
"1",
"1",
"2",
"8",
"102"
]
| [
"nonn",
"more"
]
| 26 | 1 | 3 | [
"A003513",
"A005268",
"A005269",
"A005272",
"A008926",
"A234595"
]
| null | N. J. A. Sloane, Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it) | 2015-08-06T17:42:57 | oeisdata/seq/A008/A008926.seq | 01f215096737a1cf1d966917b5b70448 |
A008927 | Number of increasing sequences of star chain type with maximal element n. | [
"1",
"1",
"1",
"2",
"3",
"6",
"10",
"20",
"36",
"70",
"130",
"252",
"475",
"916",
"1745",
"3362",
"6438",
"12410",
"23852",
"46020",
"88697",
"171339",
"330938",
"640189",
"1238751",
"2399677",
"4650819",
"9021862",
"17510819",
"34013311",
"66106491",
"128568177",
"250191797",
"487168941",
"949133722"
]
| [
"nonn"
]
| 12 | 1 | 4 | [
"A008927",
"A008928",
"A079301"
]
| null | Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it) | 2013-10-07T11:31:21 | oeisdata/seq/A008/A008927.seq | ce2e59549d5bb2cd95c9b7ab439147c2 |
A008928 | Number of increasing sequences of addition chain type with maximal element n. | [
"1",
"1",
"1",
"2",
"3",
"6",
"10",
"21",
"38",
"77",
"144",
"293",
"563",
"1131",
"2205",
"4434",
"8711",
"17466",
"34506",
"69169",
"137247",
"274677",
"546081",
"1093217",
"2177556",
"4356756",
"8688370",
"17381926",
"34691608",
"69394626",
"138578144",
"277197191",
"553794526",
"1107654097",
"2213527055"
]
| [
"nonn",
"more",
"changed"
]
| 24 | 1 | 4 | [
"A008927",
"A008928",
"A008933",
"A079301"
]
| null | Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it) | 2025-04-22T09:59:40 | oeisdata/seq/A008/A008928.seq | 3cda65263e4f49a090ed1a65bfc3f037 |
A008929 | Number of increasing sequences of Goldbach type with maximal element n. | [
"1",
"1",
"1",
"2",
"3",
"6",
"10",
"20",
"37",
"73",
"139",
"275",
"533",
"1059",
"2075",
"4126",
"8134",
"16194",
"32058",
"63910",
"126932",
"253252",
"503933",
"1006056",
"2004838",
"4004124",
"7987149",
"15957964",
"31854676",
"63660327",
"127141415",
"254136782",
"507750109",
"1015059238",
"2028564292",
"4055812657",
"8107052520"
]
| [
"nonn"
]
| 28 | 1 | 4 | [
"A008929",
"A066062",
"A164047"
]
| null | Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it) | 2023-09-13T07:21:57 | oeisdata/seq/A008/A008929.seq | 1c942e4de7cb79d62b0f469ec80131fb |
A008930 | Number of compositions (p_1, p_2, p_3, ...) of n with 1 <= p_i <= i for all i. | [
"1",
"1",
"1",
"2",
"3",
"6",
"11",
"21",
"41",
"80",
"157",
"310",
"614",
"1218",
"2421",
"4819",
"9602",
"19147",
"38204",
"76266",
"152307",
"304256",
"607941",
"1214970",
"2428482",
"4854630",
"9705518",
"19405030",
"38800412",
"77585314",
"155145677",
"310251190",
"620437691",
"1240771141",
"2481374234"
]
| [
"nonn"
]
| 79 | 0 | 4 | [
"A000707",
"A008930",
"A048285",
"A177517"
]
| null | Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it) | 2024-08-03T19:07:08 | oeisdata/seq/A008/A008930.seq | 32a103f6c341c64f07c91cfa6846d103 |
A008931 | Expansion of (2/(1+sqrt(1-36*x)))^(1/3). | [
"1",
"3",
"45",
"936",
"22572",
"592515",
"16434495",
"473825700",
"14058408519",
"426438391743",
"13164565835421",
"412255067017248",
"13064028812911440",
"418149414542496168",
"13498863325944967656",
"439006511643775469856",
"14369623854340007790108",
"473027210589699351461700"
]
| [
"nonn"
]
| 22 | 0 | 2 | null | null | N. J. A. Sloane | 2022-09-08T08:44:36 | oeisdata/seq/A008/A008931.seq | acf8e4ed5443628f95a53f9b4b31c3ed |
A008932 | Number of increasing sequences of Goldbach type of length n; a(0) = 1 by convention. | [
"1",
"1",
"2",
"5",
"17",
"65",
"292",
"1434",
"7875",
"47098",
"305226",
"2122983",
"15752080",
"124015310",
"1031857395",
"9041908204",
"83186138212"
]
| [
"nonn",
"more"
]
| 27 | 0 | 3 | [
"A008932",
"A123509"
]
| null | Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it) | 2018-04-19T15:02:12 | oeisdata/seq/A008/A008932.seq | 9f435c2c71fc7157f675ef0b031a1877 |
A008933 | Number of strictly increasing addition chains of length n. | [
"1",
"1",
"2",
"6",
"25",
"135",
"913",
"7499",
"73191",
"833597",
"10917343",
"162402263",
"2715430931",
"50576761471",
"1041203832858",
"23529845888598"
]
| [
"nonn",
"hard",
"more",
"changed"
]
| 19 | 0 | 3 | null | null | Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it) | 2025-04-22T12:19:47 | oeisdata/seq/A008/A008933.seq | 7bcd50edd9700b28a7cd98f5f490bc8a |
A008934 | Number of tournament sequences: sequences (a_1, a_2, ..., a_n) with a_1 = 1 such that a_i < a_{i+1} <= 2*a_i for all i. | [
"1",
"1",
"2",
"7",
"41",
"397",
"6377",
"171886",
"7892642",
"627340987",
"87635138366",
"21808110976027",
"9780286524758582",
"7981750158298108606",
"11950197013167283686587",
"33046443615914736611839942",
"169758733825407174485685959261",
"1627880269212042994531083889564192"
]
| [
"nonn",
"nice",
"easy"
]
| 57 | 0 | 3 | [
"A008934",
"A058222",
"A058223",
"A093655",
"A093729",
"A097710"
]
| null | Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it), Jeffrey Shallit | 2024-02-22T02:42:01 | oeisdata/seq/A008/A008934.seq | ea18b300b17cb099c929cb72d3909f75 |
A008935 | If 2n = Sum 2^e(k) then a(n) = Sum e(k)^2. | [
"1",
"4",
"5",
"9",
"10",
"13",
"14",
"16",
"17",
"20",
"21",
"25",
"26",
"29",
"30",
"25",
"26",
"29",
"30",
"34",
"35",
"38",
"39",
"41",
"42",
"45",
"46",
"50",
"51",
"54",
"55",
"36",
"37",
"40",
"41",
"45",
"46",
"49",
"50",
"52",
"53",
"56",
"57",
"61",
"62",
"65",
"66",
"61",
"62",
"65",
"66",
"70",
"71",
"74",
"75",
"77",
"78",
"81",
"82",
"86",
"87",
"90",
"91",
"49",
"50",
"53",
"54",
"58",
"59",
"62"
]
| [
"nonn",
"nice",
"easy"
]
| 38 | 1 | 2 | [
"A003995",
"A008935"
]
| null | N. J. A. Sloane | 2024-12-27T14:56:01 | oeisdata/seq/A008/A008935.seq | 798703f915b5e71634ce55566c61ebde |
A008936 | Expansion of (1 - 2*x -x^4)/(1 - 2*x)^2 in powers of x. | [
"1",
"2",
"4",
"8",
"15",
"28",
"52",
"96",
"176",
"320",
"576",
"1024",
"1792",
"3072",
"5120",
"8192",
"12288",
"16384",
"16384",
"0",
"-65536",
"-262144",
"-786432",
"-2097152",
"-5242880",
"-12582912",
"-29360128",
"-67108864",
"-150994944",
"-335544320",
"-738197504",
"-1610612736",
"-3489660928",
"-7516192768",
"-16106127360",
"-34359738368"
]
| [
"sign",
"easy"
]
| 27 | 0 | 2 | null | null | N. J. A. Sloane, Alejandro Teruel (teruel(AT)usb.ve) | 2024-03-03T04:01:23 | oeisdata/seq/A008/A008936.seq | 57591d6e4c204b832fc260d2d72d2d83 |
A008937 | a(n) = Sum_{k=0..n} T(k) where T(n) are the tribonacci numbers A000073. | [
"0",
"1",
"2",
"4",
"8",
"15",
"28",
"52",
"96",
"177",
"326",
"600",
"1104",
"2031",
"3736",
"6872",
"12640",
"23249",
"42762",
"78652",
"144664",
"266079",
"489396",
"900140",
"1655616",
"3045153",
"5600910",
"10301680",
"18947744",
"34850335",
"64099760",
"117897840",
"216847936",
"398845537",
"733591314",
"1349284788"
]
| [
"nonn",
"easy"
]
| 162 | 0 | 3 | [
"A000073",
"A000213",
"A008937",
"A018921",
"A027084",
"A055216",
"A077908",
"A140994",
"A140997",
"A209972"
]
| null | N. J. A. Sloane, Alejandro Teruel (teruel(AT)usb.ve) | 2025-03-28T11:13:36 | oeisdata/seq/A008/A008937.seq | f60ecd104322ff1eecd2ac0a19f91188 |
A008938 | Degrees of irreducible representations of group U3(3). | [
"1",
"6",
"7",
"7",
"7",
"14",
"21",
"21",
"21",
"27",
"28",
"28",
"32",
"32"
]
| [
"nonn",
"fini",
"full"
]
| 11 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008938.seq | 15156d5857063a943fcec95bd739e336 |
A008939 | Degrees of irreducible representations of group U3(4). | [
"1",
"12",
"13",
"13",
"13",
"13",
"39",
"39",
"52",
"52",
"52",
"52",
"64",
"65",
"65",
"65",
"65",
"65",
"75",
"75",
"75",
"75"
]
| [
"nonn",
"fini",
"full"
]
| 11 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008939.seq | be1e88f56877ce7efa7eb44794d4f7d4 |
A008940 | Degrees of irreducible representations of group U3(5). | [
"1",
"20",
"21",
"28",
"28",
"28",
"84",
"105",
"125",
"126",
"126",
"126",
"144",
"144"
]
| [
"nonn",
"fini",
"full"
]
| 11 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008940.seq | deef955498fabc954ec55fdc2d5ff070 |
A008941 | Degrees of irreducible representations of group U3(7). | [
"1",
"42",
"43",
"43",
"43",
"43",
"43",
"43",
"43",
"258",
"258",
"258",
"258",
"258",
"258",
"258",
"301",
"301",
"301",
"301",
"301",
"301",
"301",
"343",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344",
"344"
]
| [
"nonn",
"fini",
"full"
]
| 11 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008941.seq | 1806a39b2ced1d9261755fa6ef1ca841 |
A008942 | Degrees of irreducible representations of group U3(8). | [
"1",
"56",
"57",
"57",
"133",
"133",
"133",
"399",
"399",
"399",
"456",
"456",
"512",
"513",
"513",
"513",
"513",
"513",
"513",
"513",
"513",
"513",
"567",
"567",
"567",
"567",
"567",
"567"
]
| [
"nonn",
"fini",
"full"
]
| 11 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008942.seq | dd763f3cd12d3977709b580f34894723 |
A008943 | Degrees of irreducible representations of group U3(9). | [
"1",
"72",
"73",
"73",
"73",
"73",
"73",
"73",
"73",
"73",
"73",
"584",
"584",
"584",
"584",
"584",
"584",
"584",
"584",
"584",
"584",
"584",
"584",
"657",
"657",
"657",
"657",
"657",
"657",
"657",
"657",
"657",
"729",
"730",
"730",
"730",
"730",
"730",
"730",
"730",
"730",
"730",
"730",
"730",
"730"
]
| [
"nonn",
"fini",
"full"
]
| 13 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008943.seq | a9e17823b34caef53375f58dbf1159d5 |
A008944 | Degrees of irreducible representations of group U3(11). | [
"1",
"110",
"111",
"111",
"111",
"370",
"370",
"370",
"1110",
"1110",
"1110",
"1110",
"1110",
"1110",
"1221",
"1221",
"1221",
"1331",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332",
"1332"
]
| [
"nonn",
"fini",
"full"
]
| 13 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008944.seq | d3fed29078968895486e62e52a883f4f |
A008945 | Degrees of irreducible representations of group U4(2). | [
"1",
"5",
"5",
"6",
"10",
"10",
"15",
"15",
"20",
"24",
"30",
"30",
"30",
"40",
"40",
"45",
"45",
"60",
"64",
"81"
]
| [
"nonn",
"fini",
"full"
]
| 11 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008945.seq | 347a3ac75b9e211fd212577ed93c72c2 |
A008946 | Degrees of irreducible representations of group U4(3). | [
"1",
"21",
"35",
"35",
"90",
"140",
"189",
"210",
"280",
"280",
"280",
"280",
"315",
"315",
"420",
"560",
"640",
"640",
"729",
"896"
]
| [
"nonn",
"fini",
"full"
]
| 11 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008946.seq | b4da11a7933461e007345cbda4ed3f72 |
A008947 | Degrees of irreducible representations of group U5(2). | [
"1",
"10",
"11",
"11",
"44",
"55",
"55",
"55",
"66",
"66",
"110",
"110",
"110",
"110",
"110",
"120",
"165",
"176",
"220",
"220",
"220",
"220",
"264",
"264",
"320",
"330",
"330",
"440",
"440",
"440",
"495",
"495",
"495",
"495",
"660",
"704",
"704",
"880",
"880",
"891",
"891",
"891",
"990",
"990",
"1024",
"1215",
"1215"
]
| [
"nonn",
"fini",
"full"
]
| 11 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008947.seq | 11e801260ee3b115b19d057515af5636 |
A008948 | Degrees of irreducible representations of group U6(2). | [
"1",
"22",
"231",
"252",
"385",
"440",
"560",
"616",
"770",
"770",
"1155",
"1155",
"1155",
"1386",
"1540",
"3080",
"3080",
"3520",
"4620",
"4928",
"5544",
"6160",
"6160",
"6930",
"8064",
"9240",
"9240",
"9240",
"10395",
"10395",
"10395",
"10395",
"10395",
"11264",
"13860"
]
| [
"nonn",
"fini",
"full"
]
| 13 | 1 | 2 | null | null | N. J. A. Sloane. | 2024-06-14T22:31:09 | oeisdata/seq/A008/A008948.seq | dd8c7b39d26e41812adcab9326ada87b |
A008949 | Triangle read by rows of partial sums of binomial coefficients: T(n,k) = Sum_{i=0..k} binomial(n,i) (0 <= k <= n); also dimensions of Reed-Muller codes. | [
"1",
"1",
"2",
"1",
"3",
"4",
"1",
"4",
"7",
"8",
"1",
"5",
"11",
"15",
"16",
"1",
"6",
"16",
"26",
"31",
"32",
"1",
"7",
"22",
"42",
"57",
"63",
"64",
"1",
"8",
"29",
"64",
"99",
"120",
"127",
"128",
"1",
"9",
"37",
"93",
"163",
"219",
"247",
"255",
"256",
"1",
"10",
"46",
"130",
"256",
"382",
"466",
"502",
"511",
"512",
"1",
"11",
"56",
"176",
"386",
"638",
"848",
"968",
"1013",
"1023",
"1024",
"1",
"12",
"67",
"232",
"562",
"1024",
"1486",
"1816",
"1981",
"2036",
"2047",
"2048"
]
| [
"tabl",
"nonn",
"easy",
"nice",
"changed"
]
| 199 | 0 | 3 | [
"A000012",
"A000027",
"A000071",
"A000079",
"A000124",
"A000125",
"A000127",
"A000225",
"A000295",
"A000346",
"A001792",
"A001924",
"A002662",
"A002663",
"A002664",
"A006261",
"A007318",
"A008859",
"A008860",
"A008861",
"A008862",
"A008863",
"A008949",
"A027306",
"A035038",
"A035042",
"A055248",
"A110555",
"A163866",
"A171886",
"A228196",
"A228576",
"A249111",
"A261363"
]
| null | N. J. A. Sloane | 2025-04-22T11:06:47 | oeisdata/seq/A008/A008949.seq | d7c2ceae012a7eca5a775e2447863f93 |
A008950 | Increasing length runs of consecutive composite numbers (starting points). | [
"4",
"8",
"24",
"90",
"114",
"524",
"888",
"1130",
"1328",
"9552",
"15684",
"19610",
"31398",
"155922",
"360654",
"370262",
"492114",
"1349534",
"1357202",
"2010734",
"4652354",
"17051708",
"20831324",
"47326694",
"122164748",
"189695660",
"191912784",
"387096134",
"436273010",
"1294268492"
]
| [
"nonn",
"nice"
]
| 33 | 1 | 1 | [
"A008950",
"A008995",
"A008996"
]
| null | Mark Cramer (m.cramer(AT)qut.edu.au). Computed by Dennis Yelle (dennis(AT)netcom.com). | 2025-02-16T08:32:32 | oeisdata/seq/A008/A008950.seq | fcd3e17be783362874f0590f366b9d0b |
A008951 | Array read by columns: number of partitions of n into parts of 2 kinds. | [
"1",
"1",
"1",
"2",
"2",
"3",
"4",
"1",
"5",
"7",
"2",
"7",
"12",
"5",
"11",
"19",
"9",
"1",
"15",
"30",
"17",
"2",
"22",
"45",
"28",
"5",
"30",
"67",
"47",
"10",
"42",
"97",
"73",
"19",
"1",
"56",
"139",
"114",
"33",
"2",
"77",
"195",
"170",
"57",
"5",
"101",
"272",
"253",
"92",
"10",
"135",
"373",
"365",
"147",
"20",
"176",
"508",
"525",
"227",
"35",
"1",
"231",
"684",
"738",
"345",
"62",
"2",
"297"
]
| [
"nonn",
"tabf",
"nice"
]
| 45 | 0 | 4 | [
"A000041",
"A000070",
"A000097",
"A000098",
"A000710",
"A008951",
"A103924",
"A103929"
]
| null | N. J. A. Sloane | 2021-09-26T01:52:52 | oeisdata/seq/A008/A008951.seq | ffb12def2864cecb748c5d70a3fd4958 |
A008952 | Leading digit of 2^n. | [
"1",
"2",
"4",
"8",
"1",
"3",
"6",
"1",
"2",
"5",
"1",
"2",
"4",
"8",
"1",
"3",
"6",
"1",
"2",
"5",
"1",
"2",
"4",
"8",
"1",
"3",
"6",
"1",
"2",
"5",
"1",
"2",
"4",
"8",
"1",
"3",
"6",
"1",
"2",
"5",
"1",
"2",
"4",
"8",
"1",
"3",
"7",
"1",
"2",
"5",
"1",
"2",
"4",
"9",
"1",
"3",
"7",
"1",
"2",
"5",
"1",
"2",
"4",
"9",
"1",
"3",
"7",
"1",
"2",
"5",
"1",
"2",
"4",
"9",
"1",
"3",
"7",
"1",
"3",
"6",
"1",
"2",
"4",
"9",
"1",
"3",
"7",
"1",
"3",
"6",
"1",
"2",
"4",
"9",
"1",
"3"
]
| [
"nonn",
"base"
]
| 54 | 0 | 2 | [
"A000030",
"A000079",
"A008952"
]
| null | Leonid Broukhis | 2022-07-07T20:06:09 | oeisdata/seq/A008/A008952.seq | 304debde2a68e23fc0bf1f522a0a0e42 |
A008953 | a(n) is the leading digit of the n-th triangular number, n*(n+1)/2. | [
"1",
"3",
"6",
"1",
"1",
"2",
"2",
"3",
"4",
"5",
"6",
"7",
"9",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"5",
"5",
"5",
"6",
"6",
"7",
"7",
"7",
"8",
"8",
"9",
"9",
"9",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4"
]
| [
"nonn",
"base",
"easy"
]
| 34 | 1 | 2 | [
"A000030",
"A000217",
"A008953",
"A008954"
]
| null | N. J. A. Sloane | 2024-08-04T01:26:35 | oeisdata/seq/A008/A008953.seq | b9c6e6254459d458b0dae94412c9fae6 |
A008954 | Final digit of triangular number n*(n+1)/2. | [
"0",
"1",
"3",
"6",
"0",
"5",
"1",
"8",
"6",
"5",
"5",
"6",
"8",
"1",
"5",
"0",
"6",
"3",
"1",
"0",
"0",
"1",
"3",
"6",
"0",
"5",
"1",
"8",
"6",
"5",
"5",
"6",
"8",
"1",
"5",
"0",
"6",
"3",
"1",
"0",
"0",
"1",
"3",
"6",
"0",
"5",
"1",
"8",
"6",
"5",
"5",
"6",
"8",
"1",
"5",
"0",
"6",
"3",
"1",
"0",
"0",
"1",
"3",
"6",
"0",
"5",
"1",
"8",
"6",
"5",
"5",
"6",
"8",
"1",
"5",
"0",
"6",
"3",
"1",
"0",
"0",
"1",
"3",
"6",
"0",
"5",
"1",
"8",
"6",
"5",
"5",
"6",
"8",
"1",
"5",
"0",
"6",
"3",
"1",
"0"
]
| [
"nonn",
"base",
"easy"
]
| 43 | 0 | 3 | [
"A000217",
"A008953",
"A008954",
"A010879",
"A061501",
"A111072"
]
| null | N. J. A. Sloane | 2022-09-08T08:44:36 | oeisdata/seq/A008/A008954.seq | 7a81ea6e8183dbbe47a4d8d12d6eaebc |
A008955 | Triangle of central factorial numbers |t(2n,2n-2k)| read by rows. | [
"1",
"1",
"1",
"1",
"5",
"4",
"1",
"14",
"49",
"36",
"1",
"30",
"273",
"820",
"576",
"1",
"55",
"1023",
"7645",
"21076",
"14400",
"1",
"91",
"3003",
"44473",
"296296",
"773136",
"518400",
"1",
"140",
"7462",
"191620",
"2475473",
"15291640",
"38402064",
"25401600",
"1",
"204",
"16422",
"669188",
"14739153",
"173721912",
"1017067024",
"2483133696",
"1625702400"
]
| [
"tabl",
"nonn",
"nice",
"easy"
]
| 119 | 0 | 5 | [
"A000330",
"A000596",
"A000597",
"A001044",
"A001819",
"A001820",
"A001821",
"A002195",
"A002196",
"A008955",
"A036969",
"A101686",
"A160464",
"A160474",
"A160479",
"A161739",
"A161742",
"A161743",
"A162440",
"A162446",
"A163927",
"A234324",
"G1",
"G2"
]
| null | N. J. A. Sloane | 2023-07-11T12:04:09 | oeisdata/seq/A008/A008955.seq | 2577516a39f75baae4d056604d318c88 |
A008956 | Triangle of central factorial numbers |4^k t(2n+1,2n+1-2k)| read by rows (n>=0, k=0..n). | [
"1",
"1",
"1",
"1",
"10",
"9",
"1",
"35",
"259",
"225",
"1",
"84",
"1974",
"12916",
"11025",
"1",
"165",
"8778",
"172810",
"1057221",
"893025",
"1",
"286",
"28743",
"1234948",
"21967231",
"128816766",
"108056025",
"1",
"455",
"77077",
"6092515",
"230673443",
"3841278805",
"21878089479",
"18261468225",
"1",
"680"
]
| [
"tabl",
"nonn",
"easy"
]
| 63 | 0 | 5 | [
"A000447",
"A001147",
"A001818",
"A001823",
"A001824",
"A001825",
"A002197",
"A002198",
"A008955",
"A008956",
"A008958",
"A160479",
"A160480",
"A160487",
"A161736",
"A162443",
"A162448",
"G1"
]
| null | N. J. A. Sloane | 2020-08-24T22:40:02 | oeisdata/seq/A008/A008956.seq | 26ab32bd9c4983d746b5ff5dbf615ade |
A008957 | Triangle of central factorial numbers T(2*n,2*n-2*k), k >= 0, n >= 1 (in Riordan's notation). | [
"1",
"1",
"1",
"1",
"5",
"1",
"1",
"14",
"21",
"1",
"1",
"30",
"147",
"85",
"1",
"1",
"55",
"627",
"1408",
"341",
"1",
"1",
"91",
"2002",
"11440",
"13013",
"1365",
"1",
"1",
"140",
"5278",
"61490",
"196053",
"118482",
"5461",
"1",
"1",
"204",
"12138",
"251498",
"1733303",
"3255330",
"1071799",
"21845",
"1",
"1",
"285",
"25194",
"846260",
"10787231"
]
| [
"nonn",
"nice",
"easy",
"tabl"
]
| 52 | 1 | 5 | [
"A008955",
"A008957",
"A036969",
"A269945"
]
| null | N. J. A. Sloane | 2024-12-29T20:25:07 | oeisdata/seq/A008/A008957.seq | fa3afbdb7d62980faeb809d00709f9a4 |
A008958 | Triangle of central factorial numbers 4^k T(2n+1, 2n+1-2k). | [
"1",
"1",
"1",
"1",
"10",
"1",
"1",
"35",
"91",
"1",
"1",
"84",
"966",
"820",
"1",
"1",
"165",
"5082",
"24970",
"7381",
"1",
"1",
"286",
"18447",
"273988",
"631631",
"66430",
"1",
"1",
"455",
"53053",
"1768195",
"14057043",
"15857205",
"597871",
"1",
"1",
"680",
"129948",
"8187608",
"157280838",
"704652312",
"397027996",
"5380840",
"1"
]
| [
"nonn",
"tabl",
"easy",
"nice"
]
| 26 | 0 | 5 | [
"A000447",
"A002452",
"A002453",
"A008955",
"A008957",
"A008958",
"A036969"
]
| null | N. J. A. Sloane | 2022-01-29T01:18:59 | oeisdata/seq/A008/A008958.seq | ecff52c680abb916ab58880a67bd2166 |
A008959 | Final digit of squares: a(n) = n^2 mod 10. | [
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0",
"1",
"4",
"9",
"6",
"5",
"6",
"9",
"4",
"1",
"0"
]
| [
"nonn",
"easy",
"base"
]
| 86 | 0 | 3 | [
"A000290",
"A008959",
"A008960",
"A010879",
"A070431",
"A070435",
"A070438",
"A070442",
"A070452",
"A070514",
"A159852"
]
| null | N. J. A. Sloane, Mar 15 1996 | 2023-12-14T06:03:17 | oeisdata/seq/A008/A008959.seq | d8223adfc65384ee283f3ec6a3e0e31d |
A008960 | Final digit of cubes: n^3 mod 10. | [
"0",
"1",
"8",
"7",
"4",
"5",
"6",
"3",
"2",
"9",
"0",
"1",
"8",
"7",
"4",
"5",
"6",
"3",
"2",
"9",
"0",
"1",
"8",
"7",
"4",
"5",
"6",
"3",
"2",
"9",
"0",
"1",
"8",
"7",
"4",
"5",
"6",
"3",
"2",
"9",
"0",
"1",
"8",
"7",
"4",
"5",
"6",
"3",
"2",
"9",
"0",
"1",
"8",
"7",
"4",
"5",
"6",
"3",
"2",
"9",
"0",
"1",
"8",
"7",
"4",
"5",
"6",
"3",
"2",
"9",
"0",
"1",
"8",
"7",
"4",
"5",
"6",
"3",
"2",
"9",
"0",
"1",
"8",
"7",
"4",
"5"
]
| [
"nonn",
"easy",
"base"
]
| 59 | 0 | 3 | [
"A008959",
"A008960",
"A010879",
"A070514",
"A167176"
]
| null | N. J. A. Sloane | 2023-12-18T12:16:58 | oeisdata/seq/A008/A008960.seq | 9b1ef54edb65c0f499941acfaa25782e |
A008961 | Numerators of Taylor series for 1/(sin x + tan x). | [
"1",
"-1",
"-23",
"-947",
"-1733",
"-21781",
"-43311113",
"-2723179",
"-6414155401",
"-785453333257",
"-7699945982293",
"-66166822052531",
"-239092621861482143",
"-271166505959717",
"-74473963890443961601",
"-163219188105035970948619",
"-153312677184465775645847",
"-625566886054776334597601"
]
| [
"sign",
"frac"
]
| 12 | 0 | 3 | [
"A008961",
"A009724"
]
| null | N. J. A. Sloane | 2018-07-21T16:02:38 | oeisdata/seq/A008/A008961.seq | a04fd41e755a641f1161ce60c6b76287 |
A008962 | Number of letters in n (in Polish), excluding spaces and hyphens. | [
"4",
"5",
"3",
"4",
"6",
"4",
"5",
"6",
"5",
"8",
"8",
"10",
"9",
"10",
"11",
"10",
"10",
"12",
"11",
"14",
"11",
"16",
"14",
"15",
"17",
"15",
"16",
"17",
"16",
"19",
"11",
"16",
"14",
"15",
"17",
"15",
"16",
"17",
"16",
"19",
"12",
"17",
"15",
"16",
"18",
"16",
"17",
"18",
"17",
"20",
"12",
"17",
"15",
"16",
"18",
"16",
"17",
"18",
"17",
"20",
"13",
"18",
"16",
"17",
"19",
"17",
"18",
"19",
"18",
"21"
]
| [
"word",
"nonn"
]
| 15 | 0 | 1 | null | null | Waldemar Pompe (pompe(AT)zodiac1.mimuw.edu.pl) | 2023-01-26T11:29:13 | oeisdata/seq/A008/A008962.seq | 757d579ec5ce112601f2013016271d69 |
A008963 | Initial digit of Fibonacci number F(n). | [
"0",
"1",
"1",
"2",
"3",
"5",
"8",
"1",
"2",
"3",
"5",
"8",
"1",
"2",
"3",
"6",
"9",
"1",
"2",
"4",
"6",
"1",
"1",
"2",
"4",
"7",
"1",
"1",
"3",
"5",
"8",
"1",
"2",
"3",
"5",
"9",
"1",
"2",
"3",
"6",
"1",
"1",
"2",
"4",
"7",
"1",
"1",
"2",
"4",
"7",
"1",
"2",
"3",
"5",
"8",
"1",
"2",
"3",
"5",
"9",
"1",
"2",
"4",
"6",
"1",
"1",
"2",
"4",
"7",
"1",
"1",
"3",
"4",
"8",
"1",
"2",
"3",
"5",
"8",
"1",
"2",
"3",
"6",
"9",
"1",
"2",
"4",
"6",
"1",
"1",
"2",
"4",
"7",
"1",
"1",
"3",
"5",
"8",
"1"
]
| [
"nonn",
"base",
"easy"
]
| 37 | 0 | 4 | [
"A000030",
"A000045",
"A003893",
"A008963",
"A213201",
"A261607"
]
| null | N. J. A. Sloane. | 2025-01-05T19:51:34 | oeisdata/seq/A008/A008963.seq | 8e19129d9c8e8c776aa30afe981ff77c |
A008964 | Number of elements of order <= 2 in group of n X n upper triangular matrices over GF(2). | [
"1",
"2",
"6",
"28",
"192",
"1952",
"28800",
"618496",
"19132416",
"853508096",
"54584672256",
"5007197863936",
"656391329021952",
"122997864673574912",
"32863344789678981120",
"12522141669213840867328",
"6792468641646224590503936",
"5245768641385222636392415232"
]
| [
"nonn"
]
| 13 | 1 | 2 | null | null | Dikran Karagueuzian (dikran(AT)math.wisc.edu) | 2019-01-31T03:26:30 | oeisdata/seq/A008/A008964.seq | eb1dcfcdd64a4082461234b14082e59b |
A008965 | Number of necklaces of sets of beads containing a total of n beads. | [
"1",
"2",
"3",
"5",
"7",
"13",
"19",
"35",
"59",
"107",
"187",
"351",
"631",
"1181",
"2191",
"4115",
"7711",
"14601",
"27595",
"52487",
"99879",
"190745",
"364723",
"699251",
"1342183",
"2581427",
"4971067",
"9587579",
"18512791",
"35792567",
"69273667",
"134219795",
"260301175",
"505294127",
"981706831",
"1908881899",
"3714566311",
"7233642929"
]
| [
"nonn",
"easy",
"nice"
]
| 108 | 1 | 2 | [
"A000031",
"A008965",
"A037306",
"A057427"
]
| null | Paul Zimmermann | 2025-02-10T04:42:11 | oeisdata/seq/A008/A008965.seq | f76fabb65398a3bdf6ba11d981d41c8f |
A008966 | a(n) = 1 if n is squarefree, otherwise 0. | [
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"0",
"0"
]
| [
"easy",
"nonn",
"mult"
]
| 115 | 1 | 1 | [
"A002033",
"A005117",
"A008836",
"A008966",
"A013928",
"A020639",
"A036987",
"A047999",
"A073576",
"A082020",
"A085357",
"A087188",
"A124010",
"A156552",
"A157289",
"A157290",
"A179211",
"A179212",
"A179213",
"A179214",
"A179215",
"A212793"
]
| null | N. J. A. Sloane | 2025-02-16T08:32:32 | oeisdata/seq/A008/A008966.seq | dae89fc05f2c877e3dfa6e0b6e88890c |
A008967 | Coefficients of Gaussian polynomials q_binomial(n-2, 2). Also triangle of distribution of rank sums: Wilcoxon's statistic. Irregular triangle read by rows. | [
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"3",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"3",
"3",
"3",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"3",
"3",
"4",
"3",
"3",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"3",
"3",
"4",
"4",
"4",
"3",
"3",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"3",
"3",
"4",
"4",
"5",
"4",
"4",
"3",
"3",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"3",
"3",
"4",
"4",
"5",
"5",
"5",
"4",
"4",
"3",
"3",
"2",
"2",
"1",
"1"
]
| [
"tabf",
"nonn",
"nice",
"easy"
]
| 72 | 4 | 7 | [
"A000009",
"A004526",
"A004737",
"A008967",
"A008968",
"A047971",
"A053632",
"A068911",
"A106822",
"A167762",
"A219238",
"A238628",
"A365541",
"A365544"
]
| null | N. J. A. Sloane | 2025-02-16T08:32:32 | oeisdata/seq/A008/A008967.seq | bd33bd3b62b580a4c8cffdd5579b1395 |
A008968 | Triangle of distribution of rank sums: Wilcoxon's statistic. | [
"1",
"1",
"2",
"3",
"3",
"3",
"3",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"4",
"4",
"5",
"4",
"4",
"3",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"4",
"5",
"6",
"6",
"6",
"6",
"5",
"4",
"3",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"4",
"5",
"7",
"7",
"8",
"8",
"8",
"7",
"7",
"5",
"4",
"3",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"10",
"10",
"10",
"10",
"9",
"8",
"7",
"5",
"4",
"3",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"4",
"5",
"7",
"8",
"10",
"11",
"12",
"12",
"13",
"12"
]
| [
"tabf",
"nonn",
"nice"
]
| 16 | 6 | 3 | null | null | N. J. A. Sloane | 2021-12-16T22:35:39 | oeisdata/seq/A008/A008968.seq | 34f5f469200a735c67b7a9c6d65912a4 |
A008969 | Triangle of differences of reciprocals of unity. | [
"1",
"1",
"3",
"1",
"11",
"7",
"1",
"50",
"85",
"15",
"1",
"274",
"1660",
"575",
"31",
"1",
"1764",
"48076",
"46760",
"3661",
"63",
"1",
"13068",
"1942416",
"6998824",
"1217776",
"22631",
"127",
"1",
"109584",
"104587344",
"1744835904",
"929081776",
"30480800",
"137845",
"255",
"1",
"1026576",
"7245893376",
"673781602752",
"1413470290176",
"117550462624",
"747497920",
"833375",
"511"
]
| [
"nonn",
"tabl"
]
| 20 | 1 | 3 | [
"A000225",
"A000254",
"A000424",
"A001236",
"A001237",
"A001238",
"A001240",
"A001241",
"A001242",
"A008969"
]
| null | N. J. A. Sloane. | 2021-10-21T21:14:59 | oeisdata/seq/A008/A008969.seq | c2e885bc404aacafbed9dcbad9ff5f99 |
A008970 | Triangle T(n,k) = P(n,k)/2, n >= 2, 1 <= k < n, of one-half of number of permutations of 1..n such that the differences have k runs with the same signs. | [
"1",
"1",
"2",
"1",
"6",
"5",
"1",
"14",
"29",
"16",
"1",
"30",
"118",
"150",
"61",
"1",
"62",
"418",
"926",
"841",
"272",
"1",
"126",
"1383",
"4788",
"7311",
"5166",
"1385",
"1",
"254",
"4407",
"22548",
"51663",
"59982",
"34649",
"7936",
"1",
"510",
"13736",
"100530",
"325446",
"553410",
"517496",
"252750",
"50521",
"1",
"1022",
"42236",
"433162",
"1910706",
"4474002",
"6031076",
"4717222",
"1995181",
"353792"
]
| [
"tabl",
"nonn",
"easy",
"nice"
]
| 38 | 2 | 3 | [
"A000111",
"A000352",
"A000486",
"A000506",
"A000708",
"A008303",
"A008970",
"A059427",
"A091303",
"A360426"
]
| null | N. J. A. Sloane | 2023-02-09T09:50:34 | oeisdata/seq/A008/A008970.seq | 3488cc84968f0cf488390f12a998dd37 |
A008971 | Triangle read by rows: T(n,k) is the number of permutations of [n] with k increasing runs of length at least 2. | [
"1",
"1",
"1",
"1",
"1",
"5",
"1",
"18",
"5",
"1",
"58",
"61",
"1",
"179",
"479",
"61",
"1",
"543",
"3111",
"1385",
"1",
"1636",
"18270",
"19028",
"1385",
"1",
"4916",
"101166",
"206276",
"50521",
"1",
"14757",
"540242",
"1949762",
"1073517",
"50521",
"1",
"44281",
"2819266",
"16889786",
"17460701",
"2702765",
"1",
"132854",
"14494859"
]
| [
"tabf",
"nonn",
"easy"
]
| 168 | 0 | 6 | [
"A000340",
"A000363",
"A000364",
"A000507",
"A000708",
"A008303",
"A008970",
"A008971",
"A059427",
"A160486"
]
| null | N. J. A. Sloane | 2025-01-08T09:38:26 | oeisdata/seq/A008/A008971.seq | d684d94986b21c51b534bf359e00355a |
A008972 | n^2 raised to power n^2. | [
"1",
"256",
"387420489",
"18446744073709551616",
"88817841970012523233890533447265625",
"106387358923716524807713475752456393740167855629859291136"
]
| [
"nonn",
"easy"
]
| 35 | 1 | 2 | [
"A000290",
"A000312",
"A008972",
"A134878"
]
| null | N. J. A. Sloane | 2022-09-08T08:44:36 | oeisdata/seq/A008/A008972.seq | 44bfaabd51f452545af7c157189cfa10 |
A008973 | Fibonacci number F(n) to power F(n). | [
"1",
"1",
"1",
"4",
"27",
"3125",
"16777216",
"302875106592253",
"5842587018385982521381124421",
"11756638905368616011414050501310355554617941909569536",
"524744532468751923546122657597368049278513737089035272057324643668607677682302892208099365234375"
]
| [
"nonn"
]
| 23 | 0 | 4 | [
"A000045",
"A000312",
"A008973",
"A250495"
]
| null | N. J. A. Sloane | 2024-10-22T20:52:04 | oeisdata/seq/A008/A008973.seq | d3dda15ac3964ecf92f41680085ec9eb |
A008974 | Triangular number t(n) raised to power t(n). | [
"1",
"27",
"46656",
"10000000000",
"437893890380859375",
"5842587018385982521381124421",
"33145523113253374862572728253364605812736",
"106387358923716524807713475752456393740167855629859291136"
]
| [
"nonn"
]
| 21 | 1 | 2 | [
"A000217",
"A008974"
]
| null | N. J. A. Sloane | 2018-01-16T02:49:56 | oeisdata/seq/A008/A008974.seq | dcb5c97dbe281fc1b85af1735f26ed1a |
A008975 | Triangle, read by rows, formed by reading Pascal's triangle (A007318) mod 10. | [
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"3",
"1",
"1",
"4",
"6",
"4",
"1",
"1",
"5",
"0",
"0",
"5",
"1",
"1",
"6",
"5",
"0",
"5",
"6",
"1",
"1",
"7",
"1",
"5",
"5",
"1",
"7",
"1",
"1",
"8",
"8",
"6",
"0",
"6",
"8",
"8",
"1",
"1",
"9",
"6",
"4",
"6",
"6",
"4",
"6",
"9",
"1",
"1",
"0",
"5",
"0",
"0",
"2",
"0",
"0",
"5",
"0",
"1",
"1",
"1",
"5",
"5",
"0",
"2",
"2",
"0",
"5",
"5",
"1",
"1",
"1",
"2",
"6",
"0",
"5",
"2",
"4",
"2",
"5",
"0",
"6",
"2",
"1",
"1",
"3",
"8",
"6",
"5",
"7",
"6",
"6"
]
| [
"nonn",
"tabl",
"base"
]
| 34 | 0 | 5 | [
"A007318",
"A008975",
"A034930",
"A034931",
"A034932",
"A047999",
"A083093",
"A095140",
"A095141",
"A095142",
"A095143",
"A095144",
"A095145",
"A208134",
"A208278",
"A208279",
"A208280",
"A275198"
]
| null | N. J. A. Sloane | 2021-12-17T01:45:08 | oeisdata/seq/A008/A008975.seq | 9f06f88fff134586ecf6f475583e0709 |
A008976 | Orders of non-cyclic simple groups (divided by 4). | [
"15",
"42",
"90",
"126",
"165",
"273",
"612",
"630",
"855",
"1020",
"1404",
"1512",
"1518",
"1950",
"1980",
"2457",
"3045",
"3720",
"5040",
"6327",
"6480",
"7280",
"8184",
"8610",
"9933",
"12972",
"14700",
"15600",
"18603",
"23760",
"25665",
"28365",
"31500",
"37587",
"43890",
"44730"
]
| [
"nonn",
"easy"
]
| 18 | 1 | 1 | [
"A001034",
"A008976"
]
| [
"N2128"
]
| N. J. A. Sloane. | 2024-06-15T18:09:20 | oeisdata/seq/A008/A008976.seq | f33501d7cf38aa488cee6895e1787604 |
A008977 | a(n) = (4*n)!/(n!)^4. | [
"1",
"24",
"2520",
"369600",
"63063000",
"11732745024",
"2308743493056",
"472518347558400",
"99561092450391000",
"21452752266265320000",
"4705360871073570227520",
"1047071828879079131681280",
"235809301462142612780721600",
"53644737765488792839237440000",
"12309355935372581458927646400000"
]
| [
"nonn",
"easy",
"nice"
]
| 126 | 0 | 2 | [
"A000897",
"A000984",
"A002894",
"A002897",
"A006480",
"A008977",
"A008978",
"A008979",
"A178529",
"A186420",
"A187783",
"A188662",
"A268545",
"A268555"
]
| null | N. J. A. Sloane | 2025-02-19T13:01:30 | oeisdata/seq/A008/A008977.seq | e6b2606413d5f4a60c2ba2f5ddd035d4 |
A008978 | a(n) = (5*n)!/(n!)^5. | [
"1",
"120",
"113400",
"168168000",
"305540235000",
"623360743125120",
"1370874167589326400",
"3177459078523411968000",
"7656714453153197981835000",
"19010638202652030712978200000",
"48334775757901219912115629238400",
"125285878026462826569986857692288000"
]
| [
"nonn",
"easy"
]
| 50 | 0 | 2 | [
"A000984",
"A001460",
"A002894",
"A002897",
"A006480",
"A008977",
"A008978",
"A186420",
"A187783",
"A188662"
]
| null | N. J. A. Sloane. | 2023-07-21T17:26:50 | oeisdata/seq/A008/A008978.seq | 6c07b8fbee346df9142f6e535c77c051 |
A008979 | a(n) = (6n)!/(n!)^6. | [
"1",
"720",
"7484400",
"137225088000",
"3246670537110000",
"88832646059788350720",
"2670177736637149247308800",
"85722533226982363751829504000",
"2889253496242619386328267523990000",
"101097362223624462291180422369532000000",
"3644153415887633116359073848179365185734400",
"134567406165969006655507763343147223231094784000"
]
| [
"nonn",
"easy"
]
| 36 | 0 | 2 | [
"A000897",
"A000984",
"A002894",
"A002897",
"A006480",
"A008977",
"A008978",
"A008979",
"A071549",
"A071550",
"A071551",
"A071552",
"A186420",
"A188662"
]
| null | N. J. A. Sloane | 2024-08-17T09:01:21 | oeisdata/seq/A008/A008979.seq | 6a74aa0c2d2eca504e5d01097f759069 |
A008980 | Number of immersions of the oriented circle into the oriented plane with n double points. | [
"2",
"3",
"10",
"39",
"204",
"1262",
"8984",
"67959",
"544504",
"4535030",
"39004772",
"344217402",
"3103896536"
]
| [
"nonn",
"nice",
"more"
]
| 18 | 0 | 1 | [
"A008980",
"A008981",
"A008982",
"A008983",
"A008984",
"A008985",
"A054993"
]
| null | N. J. A. Sloane | 2020-02-26T13:38:13 | oeisdata/seq/A008/A008980.seq | cd54d70fb333f489eab6b4727df5e0f6 |
A008981 | Number of immersions of the unoriented circle into the oriented plane with n double points. | [
"1",
"2",
"5",
"21",
"102",
"639",
"4492",
"34032",
"272252",
"2267905",
"19502386",
"172111844",
"1551948268"
]
| [
"nonn",
"nice",
"hard",
"more"
]
| 33 | 0 | 2 | [
"A008980",
"A008981",
"A008982",
"A008983",
"A008984",
"A008985",
"A054993",
"A172023"
]
| null | N. J. A. Sloane | 2024-10-14T11:22:24 | oeisdata/seq/A008/A008981.seq | 45aa1b7aaa4d6512400f8724ee14891d |
A008982 | Number of immersions of the oriented circle into the unoriented plane with n double points. | [
"1",
"2",
"5",
"21",
"102",
"640",
"4492",
"34047",
"272252",
"2268085",
"19502386",
"172113886",
"1551948268"
]
| [
"nonn",
"nice"
]
| 13 | 0 | 2 | [
"A008980",
"A008981",
"A008982",
"A008983",
"A008984",
"A008985",
"A054993"
]
| null | N. J. A. Sloane | 2018-04-19T17:00:43 | oeisdata/seq/A008/A008982.seq | 607854a53be1830baeb36ea274f5f896 |
A008983 | Number of immersions of the unoriented circle into the unoriented plane with n double points. | [
"1",
"2",
"5",
"20",
"82",
"435",
"2645",
"18489",
"141326",
"1153052",
"9819315",
"86305315",
"776868505"
]
| [
"nonn",
"nice",
"more"
]
| 29 | 0 | 2 | [
"A008980",
"A008981",
"A008982",
"A008983",
"A008984",
"A008985",
"A008989",
"A054993",
"A118814"
]
| null | N. J. A. Sloane | 2024-10-14T11:22:38 | oeisdata/seq/A008/A008983.seq | 8642f6cbbf477674d8531d1d558816a0 |
A008984 | Number of immersions of the oriented circle into the oriented plane with n double points and index n-1. | [
"1",
"1",
"3",
"10",
"35",
"133",
"538",
"2144",
"8643",
"34690",
"139122",
"556618"
]
| [
"nonn",
"nice",
"more"
]
| 20 | 0 | 3 | [
"A008980",
"A008981",
"A008982",
"A008983",
"A008984",
"A008985",
"A054993"
]
| null | N. J. A. Sloane | 2025-01-22T00:05:47 | oeisdata/seq/A008/A008984.seq | 2995807139f4db30817abbc791201a18 |
A008985 | Triangle T(n,k) giving number of immersions of the oriented circle into the oriented plane with n double points and index k, k = -n-1, -n+1, ..., n-1, n+1. | [
"0",
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"3",
"2",
"4",
"10",
"11",
"10",
"4",
"10",
"35",
"57",
"57",
"35",
"10",
"26",
"133",
"290",
"364",
"290",
"133",
"26",
"80",
"538",
"1504",
"2370",
"2370",
"1504",
"538",
"80",
"246",
"2144",
"7607",
"14846",
"18273",
"14846",
"7607",
"2144",
"246",
"810",
"8643",
"37762",
"90182",
"134855",
"134855",
"90182",
"37762",
"8643",
"810"
]
| [
"nonn",
"nice",
"tabl"
]
| 27 | -1 | 7 | [
"A003239",
"A008980",
"A008981",
"A008982",
"A008983",
"A008984",
"A008985",
"A054993"
]
| null | N. J. A. Sloane | 2025-01-22T01:59:56 | oeisdata/seq/A008/A008985.seq | b852718f5e54b1c165c69143869445ef |
A008986 | Number of immersions of oriented circle into oriented sphere with n double points. | [
"1",
"1",
"3",
"9",
"37",
"182",
"1143",
"7553",
"54559",
"412306",
"3251240",
"26478264",
"221714164",
"1900103364",
"16613990484",
"147816411921",
"1335367515821"
]
| [
"nonn",
"more"
]
| 57 | 0 | 3 | [
"A008986",
"A008987",
"A008988",
"A008989",
"A260285"
]
| null | N. J. A. Sloane | 2024-03-30T11:39:29 | oeisdata/seq/A008/A008986.seq | b6dfc08f858d05e1c428db6ec42cea36 |
A008987 | Number of immersions of an unoriented circle into the oriented sphere with n double points. | [
"1",
"1",
"2",
"6",
"21",
"99",
"588",
"3829",
"27404",
"206543",
"1626638",
"13242275",
"110865868",
"950078474",
"8307074080",
"73908443799",
"667684486429"
]
| [
"nonn",
"more"
]
| 53 | 0 | 3 | [
"A008986",
"A008987",
"A008988",
"A008989",
"A260848"
]
| null | N. J. A. Sloane | 2024-03-30T12:15:26 | oeisdata/seq/A008/A008987.seq | 768d607764a370e387007d69212b0920 |
A008988 | Number of immersions of oriented circle into unoriented sphere with n double points. | [
"1",
"1",
"2",
"6",
"21",
"97",
"579",
"3812",
"27328",
"206410",
"1625916",
"13241177",
"110859326",
"950069179",
"8307012899",
"73908363060",
"667683905600"
]
| [
"nonn",
"nice",
"more"
]
| 47 | 0 | 3 | [
"A008986",
"A008987",
"A008988",
"A008989",
"A260885"
]
| null | N. J. A. Sloane | 2024-03-29T12:45:02 | oeisdata/seq/A008/A008988.seq | 8272b918b6d871d01ca4e5b84fbfd4f1 |
A008989 | Number of immersions of an unoriented circle into the unoriented sphere with n double points. | [
"1",
"1",
"2",
"6",
"19",
"76",
"376",
"2194",
"14614",
"106421",
"823832",
"6657811",
"55557329",
"475475046",
"4155030702",
"36959470662",
"333860366236"
]
| [
"nonn",
"more"
]
| 68 | 0 | 3 | [
"A008986",
"A008987",
"A008988",
"A008989",
"A260914",
"A264759",
"A277739"
]
| null | N. J. A. Sloane | 2024-03-30T12:17:55 | oeisdata/seq/A008/A008989.seq | 7dcd52dc9d6283ac081bac7f8d9338b8 |
A008990 | Numerators of sequence having sqrt(cos(x)) as e.g.f. (even-indexed coefficients only). | [
"1",
"-1",
"-1",
"-19",
"-559",
"-29161",
"-2368081",
"-276580459",
"-43947282079",
"-9118829535121",
"-2394495729300961",
"-776228170682260099",
"-304471093666800990799",
"-142128398853646068197881",
"-77865168574139358455774641",
"-49474260304294496117945326939"
]
| [
"sign",
"frac",
"easy",
"nice"
]
| 53 | 0 | 4 | [
"A000079",
"A008990",
"A027641"
]
| null | N. J. A. Sloane | 2022-04-15T13:02:16 | oeisdata/seq/A008/A008990.seq | 9489db6d2524c8776cdfe85dacfc066a |
A008991 | Numerators of coefficients in expansion of sqrt(sin(x)/x) (even powers only). | [
"1",
"-1",
"1",
"-1",
"-67",
"-1",
"-64397",
"-113249",
"-3679787",
"-810304169",
"-6040635661561",
"-428305999661",
"-16827172241810597",
"-5620292762592913",
"-1550760014054450957",
"-4168373361283100017",
"-8551022502876237590534947"
]
| [
"sign"
]
| 33 | 0 | 5 | [
"A008991",
"A008992",
"A220002",
"A220466"
]
| null | N. J. A. Sloane | 2025-02-16T08:32:32 | oeisdata/seq/A008/A008991.seq | c6e3ac95ceed3df9c0f4bc313581d0d8 |
A008992 | Denominators of coefficients in expansion of sqrt(sin(x)/x) (even powers only). | [
"1",
"12",
"1440",
"24192",
"29030400",
"5677056",
"4649508864000",
"100429391462400",
"39023992111104000",
"100609855353520128000",
"8632325589332026982400000",
"6946127879462505676800000",
"3060839851788186207387648000000"
]
| [
"nonn"
]
| 28 | 0 | 2 | [
"A008991",
"A008992",
"A220002",
"A220466"
]
| null | N. J. A. Sloane | 2020-03-16T14:24:23 | oeisdata/seq/A008/A008992.seq | 007909c7a5f447709a6a83044e1c3b1d |
A008993 | Numerators of coefficients in expansion of cube root of sin(x). | [
"1",
"-1",
"-1",
"-53",
"-191",
"-20353",
"-16080599",
"-2454263",
"-1929502811",
"-234796649489321",
"-5861873873476337",
"-216960814836289519",
"-709848919641928941541",
"-3162120754204994494571",
"-2121145877577124094947",
"-25314492944947070077552347103",
"-1647232883667178291585597345249"
]
| [
"sign"
]
| 10 | 0 | 4 | null | null | N. J. A. Sloane | 2018-07-21T23:37:40 | oeisdata/seq/A008/A008993.seq | dc38b0c3b350dc64eb814fd48ec54586 |
A008994 | Denominators of coefficients in expansion of cube root of sin(x). | [
"1",
"18",
"3240",
"1224720",
"62985600",
"87298041600",
"857965152844800",
"1575854362368000",
"14540529421135872000",
"20363866049006577377280000",
"5760064968147574743859200000",
"2384666896813095943957708800000"
]
| [
"nonn"
]
| 9 | 0 | 2 | null | null | N. J. A. Sloane | 2018-07-21T16:23:43 | oeisdata/seq/A008/A008994.seq | 8b4a8884ee9ac08dfa40793dcbd0d6a6 |
A008995 | Increasing length runs of consecutive composite numbers (endpoints). | [
"4",
"10",
"28",
"96",
"126",
"540",
"906",
"1150",
"1360",
"9586",
"15726",
"19660",
"31468",
"156006",
"360748",
"370372",
"492226",
"1349650",
"1357332",
"2010880",
"4652506",
"17051886",
"20831532",
"47326912",
"122164968",
"189695892",
"191913030"
]
| [
"nonn"
]
| 26 | 1 | 1 | [
"A000101",
"A008950",
"A008995",
"A008996"
]
| null | Mark Cramer (m.cramer(AT)qut.edu.au). Computed by Dennis Yelle (dennis(AT)netcom.com). | 2025-02-16T08:32:32 | oeisdata/seq/A008/A008995.seq | 9a5a28f4a95bf5999f0a63c781603d2a |
A008996 | Increasing length runs of consecutive composite numbers (records). | [
"1",
"3",
"5",
"7",
"13",
"17",
"19",
"21",
"33",
"35",
"43",
"51",
"71",
"85",
"95",
"111",
"113",
"117",
"131",
"147",
"153",
"179",
"209",
"219",
"221",
"233",
"247",
"249",
"281",
"287",
"291",
"319",
"335",
"353",
"381",
"383",
"393",
"455",
"463",
"465",
"473",
"485",
"489",
"499",
"513",
"515",
"531",
"533",
"539",
"581",
"587",
"601",
"651",
"673",
"715",
"765"
]
| [
"nonn",
"nice"
]
| 39 | 1 | 2 | [
"A005250",
"A008950",
"A008995",
"A008996",
"A010051",
"A046933",
"A058320"
]
| null | Mark Cramer (m.cramer(AT)qut.edu.au), Mar 15 1996 | 2025-02-16T08:32:32 | oeisdata/seq/A008/A008996.seq | 855646b1cb683bbea11d52108a6d0db3 |
A008997 | Orchard problem with 5 trees in a row (may not have all been proved optimal). | [
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"3",
"3",
"4",
"6",
"6",
"7",
"9",
"10",
"11"
]
| [
"nonn",
"nice",
"more"
]
| 24 | 1 | 9 | [
"A003035",
"A006065",
"A008997"
]
| null | N. J. A. Sloane | 2025-02-16T08:32:32 | oeisdata/seq/A008/A008997.seq | d1d58d8eef4b4b5e4f994dad80a486f5 |
A008998 | a(n) = 2*a(n-1) + a(n-3), with a(0)=1 and a(1)=2. | [
"1",
"2",
"4",
"9",
"20",
"44",
"97",
"214",
"472",
"1041",
"2296",
"5064",
"11169",
"24634",
"54332",
"119833",
"264300",
"582932",
"1285697",
"2835694",
"6254320",
"13794337",
"30424368",
"67103056",
"148000449",
"326425266",
"719953588",
"1587907625",
"3502240516",
"7724434620",
"17036776865",
"37575794246"
]
| [
"nonn",
"easy"
]
| 73 | 0 | 2 | [
"A008998",
"A052980",
"A077852",
"A077926"
]
| null | N. J. A. Sloane | 2022-09-08T08:44:37 | oeisdata/seq/A008/A008998.seq | 623a667cdb0539a29808a1d3a45583ff |
A008999 | a(n) = 2*a(n-1) + a(n-4). | [
"1",
"2",
"4",
"8",
"17",
"36",
"76",
"160",
"337",
"710",
"1496",
"3152",
"6641",
"13992",
"29480",
"62112",
"130865",
"275722",
"580924",
"1223960",
"2578785",
"5433292",
"11447508",
"24118976",
"50816737",
"107066766",
"225581040",
"475281056",
"1001378849"
]
| [
"nonn",
"easy"
]
| 48 | 0 | 2 | [
"A008998",
"A008999"
]
| null | N. J. A. Sloane | 2022-10-21T22:05:17 | oeisdata/seq/A008/A008999.seq | a5837f8e529255621e414f8065a99576 |
A009000 | Ordered hypotenuse numbers (squares are sums of 2 distinct nonzero squares). | [
"5",
"10",
"13",
"15",
"17",
"20",
"25",
"25",
"26",
"29",
"30",
"34",
"35",
"37",
"39",
"40",
"41",
"45",
"50",
"50",
"51",
"52",
"53",
"55",
"58",
"60",
"61",
"65",
"65",
"65",
"65",
"68",
"70",
"73",
"74",
"75",
"75",
"78",
"80",
"82",
"85",
"85",
"85",
"85",
"87",
"89",
"90",
"91",
"95",
"97",
"100",
"100",
"101",
"102",
"104",
"105",
"106",
"109",
"110",
"111",
"113",
"115",
"116",
"117",
"119",
"120"
]
| [
"nonn",
"nice",
"easy"
]
| 87 | 1 | 1 | [
"A004144",
"A004431",
"A006339",
"A009000",
"A009003",
"A009012",
"A024507",
"A046083",
"A046084",
"A083025",
"A084645",
"A084646",
"A084647",
"A084648",
"A084649"
]
| null | David W. Wilson | 2025-02-16T08:32:32 | oeisdata/seq/A009/A009000.seq | 1bf01379bec77d9552790eba4f76161a |
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