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A005501 | Number of unrooted triangulations of a pentagon with n internal nodes. | [
"1",
"4",
"14",
"69",
"396",
"2503",
"16905",
"119571",
"874771",
"6567181",
"50329363",
"392328944",
"3102523829",
"24839151315",
"201011560316",
"1642124006250",
"13527821578754",
"112279051170871",
"938188211057701",
"7887160187935198",
"66672792338916470",
"566452703137103796",
"4834838039006782636"
] | [
"nonn"
] | 36 | 0 | 2 | [
"A002711",
"A005501",
"A005506",
"A169808"
] | [
"M3488"
] | N. J. A. Sloane | 2021-02-23T10:06:09 | oeisdata/seq/A005/A005501.seq | ea20a1a2498f5ac44ebc4d174be011c8 |
A005502 | Number of unrooted triangulations of a hexagon with n internal nodes. | [
"3",
"11",
"53",
"295",
"1867",
"12560",
"89038",
"652198",
"4903955",
"37627699",
"293607612",
"2323604832",
"18614121391",
"150704813812",
"1231596828200",
"10148762396401",
"84252059397251",
"704122279126074",
"5920239345451780",
"50051285956517452",
"425273487358680290",
"3630084126997807369"
] | [
"nonn"
] | 35 | 0 | 1 | [
"A005495",
"A005502",
"A005507",
"A169808"
] | [
"M2904"
] | N. J. A. Sloane | 2021-02-23T10:06:16 | oeisdata/seq/A005/A005502.seq | b2565dabe74ac6313c929f9f77af3161 |
A005503 | Number of unrooted triangulations of a disk with one internal node and n+3 nodes on the boundary. | [
"1",
"2",
"4",
"11",
"28",
"91",
"291",
"1004",
"3471",
"12350",
"44114",
"159519",
"579835",
"2121845",
"7800702",
"28813730",
"106844383",
"397647256",
"1484755972",
"5560561040",
"20881939915",
"78617991116",
"296678132514",
"1121988213996",
"4251702739831",
"16141719280994",
"61389611762126",
"233856524866209"
] | [
"nonn"
] | 30 | 0 | 2 | [
"A005503",
"A169808"
] | [
"M1248"
] | N. J. A. Sloane | 2021-02-23T10:06:24 | oeisdata/seq/A005/A005503.seq | d5499ed044ed4dfbc46fc19889547f50 |
A005504 | Number of unrooted triangulations of a disk with 2 internal nodes and n+3 nodes on the boundary. | [
"1",
"5",
"14",
"53",
"178",
"685",
"2548",
"9876",
"37950",
"147520",
"572594",
"2230735",
"8693932",
"33939465",
"132598484",
"518607032",
"2029990774",
"7952788446",
"31179668572",
"122331725930",
"480283816348",
"1886829349570",
"7416950176904",
"29171683995320",
"114795961678380",
"451968102200966",
"1780298693036010"
] | [
"nonn"
] | 25 | 0 | 2 | [
"A005504",
"A169808"
] | [
"M3846"
] | N. J. A. Sloane | 2021-02-23T10:06:35 | oeisdata/seq/A005/A005504.seq | c6746330a02e9fcddcf957e517b87a2c |
A005505 | Number of unrooted triangulations with reflection symmetry of a quadrilateral with n internal nodes. | [
"1",
"2",
"4",
"10",
"29",
"86",
"266",
"844",
"2742",
"9032",
"30202",
"101988",
"347914",
"1195500",
"4138310",
"14405848",
"50428392",
"177321636",
"626250990",
"2219876580",
"7896651847",
"28176271634",
"100830069380",
"361757157484",
"1301092926454",
"4689840961196",
"16940093338162",
"61305930699382"
] | [
"nonn"
] | 40 | 0 | 2 | [
"A002710",
"A005500",
"A005505",
"A169809"
] | [
"M1227"
] | N. J. A. Sloane | 2021-02-23T10:06:45 | oeisdata/seq/A005/A005505.seq | 0a472253cd7702f90da492e969a254ad |
A005506 | Number of unrooted triangulations with reflection symmetry of a pentagon with n internal nodes. | [
"1",
"3",
"7",
"19",
"57",
"176",
"557",
"1806",
"5954",
"19897",
"67235",
"229366",
"788688",
"2730810",
"9512107",
"33309444",
"117190184",
"414039578",
"1468349782",
"5225201321",
"18651958885",
"66769742002",
"239643164237",
"862168692562",
"3108716586702",
"11232127258416",
"40660388117380",
"147453014455094"
] | [
"nonn"
] | 37 | 0 | 2 | [
"A002711",
"A005501",
"A005506",
"A169809"
] | [
"M2676"
] | N. J. A. Sloane | 2021-02-23T10:07:00 | oeisdata/seq/A005/A005506.seq | bd27f2c76628fbfedc6dcc03a1d34060 |
A005507 | Number of unrooted triangulations with reflection symmetry of a hexagon with n internal nodes. | [
"2",
"6",
"18",
"52",
"166",
"524",
"1722",
"5664",
"19072",
"64408",
"220676",
"758864",
"2634734",
"9180872",
"32208376",
"113371636",
"401067522",
"1423073892",
"5068961452",
"18103192360",
"64853607912",
"232872927444",
"838311889890",
"3023961593292",
"10931277735230",
"39586258360246",
"143617299291242"
] | [
"nonn"
] | 33 | 0 | 1 | [
"A005495",
"A005502",
"A005507",
"A169809"
] | [
"M1622"
] | N. J. A. Sloane | 2021-02-23T10:07:10 | oeisdata/seq/A005/A005507.seq | 04e3171dd1f4b5348ad4a79024b850bf |
A005508 | Number of unrooted triangulations with reflection symmetry of a disk with one internal node and n+3 nodes on the boundary. | [
"1",
"2",
"3",
"6",
"8",
"18",
"23",
"56",
"70",
"180",
"222",
"594",
"726",
"2002",
"2431",
"6864",
"8294",
"23868",
"28730",
"83980",
"100776",
"298452",
"357238",
"1069776",
"1277788",
"3863080",
"4605980",
"14040810",
"16715250",
"51325650",
"61020495",
"188574240",
"223931910",
"695987820",
"825632610",
"2579248980"
] | [
"nonn"
] | 23 | 0 | 2 | [
"A005508",
"A169809"
] | [
"M0755"
] | N. J. A. Sloane | 2021-02-23T10:07:19 | oeisdata/seq/A005/A005508.seq | 610cced68f09a4c6962cbd0daabb61dc |
A005509 | Number of unrooted triangulations with reflection symmetry of a disk with 2 internal nodes and n+3 nodes on the boundary. | [
"1",
"4",
"7",
"18",
"26",
"68",
"91",
"248",
"318",
"900",
"1122",
"3278",
"4004",
"12012",
"14443",
"44304",
"52598",
"164424",
"193154",
"613700",
"714476",
"2302344",
"2659582",
"8677072",
"9954860",
"32836180",
"37442160",
"124715430",
"141430680",
"475237500",
"536257995",
"1816267680",
"2040199590",
"6959878200"
] | [
"nonn"
] | 22 | 0 | 2 | [
"A005509",
"A169809"
] | [
"M3312"
] | N. J. A. Sloane | 2021-02-23T10:07:27 | oeisdata/seq/A005/A005509.seq | 9c701eae5d498d36dd4b0861e4cc5eea |
A005510 | a(n) = 1 + a(floor(n/2))*a(ceiling(n/2)) for n > 1, a(1) = 3. | [
"3",
"10",
"31",
"101",
"311",
"962",
"3132",
"10202",
"31412",
"96722",
"299183",
"925445",
"3012985",
"9809425",
"31952665",
"104080805",
"320465225",
"986713745",
"3038231465",
"9355145285",
"28937578127",
"89510467490",
"276877411436",
"856448448026",
"2788351903326",
"9078078610226",
"29555650383626"
] | [
"nonn",
"easy"
] | 18 | 1 | 1 | [
"A005468",
"A005469",
"A005510"
] | [
"M2842"
] | Colin Mallows | 2019-07-04T15:47:46 | oeisdata/seq/A005/A005510.seq | 887142492f73a215640551a685265b7e |
A005511 | a(n) = 1 + a(floor(n/2))*a(ceiling(n/2)) for n > 1, a(1) = 4. | [
"4",
"17",
"69",
"290",
"1174",
"4762",
"20011",
"84101",
"340461",
"1378277",
"5590589",
"22676645",
"95292383",
"400440122",
"1682945112",
"7072978202",
"28633110562",
"115913692522",
"469249565698",
"1899647488730",
"7705380235154",
"31254685366922",
"126775802093906",
"514230228456026",
"2160911540495036"
] | [
"nonn",
"nice"
] | 29 | 1 | 1 | null | [
"M3536"
] | Colin Mallows | 2019-07-04T15:46:50 | oeisdata/seq/A005/A005511.seq | eaf8867dfc272c8fc8c29e2504c8d61c |
A005512 | Number of series-reduced labeled trees with n nodes. | [
"1",
"1",
"0",
"4",
"5",
"96",
"427",
"6448",
"56961",
"892720",
"11905091",
"211153944",
"3692964145",
"75701219608",
"1613086090995",
"38084386700896",
"949168254452993",
"25524123909350112",
"725717102391257347",
"21955114496683796680"
] | [
"nonn",
"nice"
] | 75 | 1 | 4 | [
"A000014",
"A005512",
"A060313"
] | [
"M3261"
] | N. J. A. Sloane, Simon Plouffe | 2025-02-16T08:32:28 | oeisdata/seq/A005/A005512.seq | e1f59c77125bdacc024c126ee9f4b6c8 |
A005513 | Number of n-bead bracelets (turnover necklaces) of two colors with 6 red beads and n-6 black beads. | [
"1",
"1",
"4",
"7",
"16",
"26",
"50",
"76",
"126",
"185",
"280",
"392",
"561",
"756",
"1032",
"1353",
"1782",
"2277",
"2920",
"3652",
"4576",
"5626",
"6916",
"8372",
"10133",
"12103",
"14448",
"17063",
"20128",
"23528",
"27474",
"31824",
"36822",
"42315",
"48564",
"55404",
"63133",
"71554",
"81004"
] | [
"nonn",
"easy",
"nice"
] | 101 | 6 | 3 | [
"A005513",
"A052307"
] | [
"M3311"
] | N. J. A. Sloane | 2025-02-26T11:24:08 | oeisdata/seq/A005/A005513.seq | 9e4e600e8138688dde30a14d4f93875d |
A005514 | Number of n-bead bracelets (turnover necklaces) with 8 red beads and n-8 black beads. | [
"1",
"1",
"5",
"10",
"29",
"57",
"126",
"232",
"440",
"750",
"1282",
"2052",
"3260",
"4950",
"7440",
"10824",
"15581",
"21879",
"30415",
"41470",
"56021",
"74503",
"98254",
"127920",
"165288",
"211276",
"268228",
"337416",
"421856",
"523260",
"645456",
"790704",
"963793",
"1167645",
"1408185"
] | [
"nonn",
"easy",
"nice"
] | 148 | 8 | 3 | [
"A005514",
"A008805",
"A032193",
"A032279",
"A032280",
"A032281",
"A032282",
"A052307",
"A119963",
"A292906"
] | [
"M3801"
] | N. J. A. Sloane | 2025-02-26T11:14:07 | oeisdata/seq/A005/A005514.seq | b2bc37704d0748de340067efee7d59f8 |
A005515 | Number of n-bead bracelets (turnover necklaces) of two colors with 10 red beads and n-10 black beads. | [
"1",
"1",
"6",
"14",
"47",
"111",
"280",
"600",
"1282",
"2494",
"4752",
"8524",
"14938",
"25102",
"41272",
"65772",
"102817",
"156871",
"235378",
"346346",
"502303",
"716859",
"1010256",
"1404624",
"1931540",
"2625658",
"3534776",
"4711448",
"6226148",
"8156396",
"10603704",
"13679696",
"17527595",
"22304765",
"28209566",
"35459694"
] | [
"nonn"
] | 79 | 10 | 3 | [
"A005515",
"A052307"
] | [
"M4105"
] | N. J. A. Sloane | 2025-04-02T05:15:56 | oeisdata/seq/A005/A005515.seq | ee6426acf9743ee2f5aebcec0b8faeba |
A005516 | Number of n-bead bracelets (turnover necklaces) with 12 red beads. | [
"1",
"1",
"7",
"19",
"72",
"196",
"561",
"1368",
"3260",
"7105",
"14938",
"29624",
"56822",
"104468",
"186616",
"322786",
"544802",
"896259",
"1444147",
"2278640",
"3532144",
"5380034",
"8070400",
"11926928",
"17393969",
"25042836",
"35638596",
"50152013",
"69855536"
] | [
"nonn"
] | 73 | 12 | 3 | [
"A005516",
"A052307"
] | [
"M4368"
] | N. J. A. Sloane | 2025-02-26T11:22:14 | oeisdata/seq/A005/A005516.seq | ff1cb4a5f08a634b76e9eb2d291d835a |
A005517 | Smallest label f(T) given to a rooted tree T with n nodes in Matula-Goebel labeling. | [
"1",
"2",
"3",
"5",
"9",
"15",
"25",
"45",
"75",
"125",
"225",
"375",
"625",
"1125",
"1875",
"3125",
"5625",
"9375",
"15625",
"28125",
"46875",
"78125",
"140625",
"234375",
"390625",
"703125",
"1171875",
"1953125",
"3515625",
"5859375",
"9765625",
"17578125",
"29296875",
"48828125"
] | [
"nonn",
"easy",
"nice"
] | 67 | 1 | 2 | [
"A005517",
"A005518",
"A061773"
] | [
"M0706"
] | N. J. A. Sloane | 2022-03-09T09:05:57 | oeisdata/seq/A005/A005517.seq | 2228b7a76a8a72df5ab622586867fe37 |
A005518 | Largest label f(T) given to a rooted tree T with n nodes in Matula-Goebel labeling. | [
"1",
"2",
"4",
"8",
"19",
"67",
"331",
"2221",
"19577",
"219613",
"3042161",
"50728129",
"997525853",
"22742734291",
"592821132889",
"17461204521323",
"575411103069067",
"21034688742654437",
"846729487306354343"
] | [
"nonn"
] | 50 | 1 | 2 | [
"A005517",
"A005518",
"A057452",
"A061773"
] | [
"M1154"
] | N. J. A. Sloane | 2022-01-24T07:11:34 | oeisdata/seq/A005/A005518.seq | 83e1470565677de606ed440c61298359 |
A005519 | Let T(n,d) = number of distinct d-dimensional polyominoes (or polycubes) with n cells (A049429, A049430); sequence gives Sum_{d} T(n,d). | [
"1",
"1",
"2",
"7",
"26",
"153",
"1134",
"11050",
"128987",
"1765252",
"27418060"
] | [
"nonn",
"nice",
"hard",
"more"
] | 24 | 1 | 3 | [
"A005519",
"A049429",
"A049430"
] | [
"M1775"
] | N. J. A. Sloane | 2022-01-31T01:40:29 | oeisdata/seq/A005/A005519.seq | c1cdd9e66f6228a6f428c58b201d304e |
A005520 | Smallest number of complexity n: smallest number requiring n 1's to build using + and *. | [
"1",
"2",
"3",
"4",
"5",
"7",
"10",
"11",
"17",
"22",
"23",
"41",
"47",
"59",
"89",
"107",
"167",
"179",
"263",
"347",
"467",
"683",
"719",
"1223",
"1438",
"1439",
"2879",
"3767",
"4283",
"6299",
"10079",
"11807",
"15287",
"21599",
"33599",
"45197",
"56039",
"81647",
"98999",
"163259",
"203999",
"241883",
"371447",
"540539",
"590399",
"907199"
] | [
"nonn",
"nice"
] | 114 | 1 | 2 | [
"A003037",
"A005245",
"A005421",
"A005520",
"A025280",
"A048183",
"A181898",
"A182061",
"A265360"
] | [
"M0523"
] | N. J. A. Sloane | 2025-02-16T08:32:28 | oeisdata/seq/A005/A005520.seq | e075d204fdd5c724ad250f009e778e42 |
A005521 | 1 + (sum of first n odd primes - n)/2. | [
"1",
"2",
"4",
"7",
"12",
"18",
"26",
"35",
"46",
"60",
"75",
"93",
"113",
"134",
"157",
"183",
"212",
"242",
"275",
"310",
"346",
"385",
"426",
"470",
"518",
"568",
"619",
"672",
"726",
"782",
"845",
"910",
"978",
"1047",
"1121",
"1196",
"1274",
"1355",
"1438",
"1524",
"1613",
"1703",
"1798"
] | [
"nonn"
] | 9 | 0 | 2 | [
"A005521",
"A065917"
] | null | N. J. A. Sloane. | 2022-06-25T22:52:27 | oeisdata/seq/A005/A005521.seq | ffb41d194a71617882f449ba6fcd03a4 |
A005522 | a(n) = 1 + L(n) + F(2*n-1) with {L(n)}_{n>=0} the Lucas numbers (A000032) and F(2*n-1)_{n>=0} the bisected Fibonacci numbers (A001519). | [
"4",
"3",
"6",
"10",
"21",
"46",
"108",
"263",
"658",
"1674",
"4305",
"11146",
"28980",
"75547",
"197262",
"515594",
"1348477",
"3528150",
"9233244",
"24167167",
"63261114",
"165604618",
"433534041",
"1134967250",
"2971318756",
"7778909811",
"20365282518",
"53316730378",
"139584573093",
"365436446014",
"956723886540"
] | [
"nonn",
"easy"
] | 105 | 0 | 1 | [
"A000032",
"A000045",
"A001519",
"A001622",
"A005522",
"A006172",
"A079586",
"A254884"
] | [
"M2537"
] | N. J. A. Sloane | 2025-01-05T19:51:33 | oeisdata/seq/A005/A005522.seq | 4c001c4ad0c78b628158472e5dcd2750 |
A005523 | a(n) = maximal number of rational points on an elliptic curve over GF(q), where q = A246655(n) is the n-th prime power > 1. | [
"5",
"7",
"9",
"10",
"13",
"14",
"16",
"18",
"21",
"25",
"26",
"28",
"33",
"36",
"38",
"40",
"43",
"44",
"50",
"54",
"57",
"61",
"64",
"68",
"75",
"77",
"81",
"84",
"88",
"91",
"97",
"100",
"102",
"108",
"117",
"122",
"124",
"128",
"130",
"135",
"144",
"148",
"150",
"150",
"154",
"161",
"163",
"174",
"176",
"183",
"189",
"193",
"196",
"200",
"206",
"208",
"219",
"221",
"226",
"228",
"241",
"253",
"258",
"260"
] | [
"nonn",
"easy"
] | 51 | 1 | 1 | [
"A000961",
"A005523",
"A246655"
] | [
"M3757"
] | N. J. A. Sloane | 2025-02-16T08:32:28 | oeisdata/seq/A005/A005523.seq | 4c4da87a861875298eb1800e7303e258 |
A005524 | Values k arising from a construction of Hirschfeld of k-arcs on elliptic curves over GF(q), where q = A246655(n) is the n-th prime power > 1. | [
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"12",
"13",
"14",
"16",
"18",
"19",
"20",
"21",
"22",
"25",
"27",
"28",
"30",
"32",
"34",
"37",
"38",
"40",
"42",
"44",
"45",
"48",
"50",
"51",
"54",
"58",
"61",
"62",
"64",
"65",
"67",
"72",
"74",
"75",
"75",
"77",
"80",
"81",
"87",
"88",
"91",
"94",
"96",
"98",
"100",
"103",
"104",
"109",
"110",
"113",
"114",
"120",
"126",
"129",
"130",
"132",
"135",
"136",
"137",
"141"
] | [
"nonn"
] | 31 | 1 | 1 | [
"A000961",
"A005523",
"A005524",
"A365216"
] | [
"M0475"
] | N. J. A. Sloane. | 2023-08-27T10:35:41 | oeisdata/seq/A005/A005524.seq | b76d93498633b33e548d869bba8d7ba2 |
A005525 | Maximal number of rational points on a curve of genus 2 over GF(q), where q = A246655(n) is the n-th prime power > 1. | [
"6",
"8",
"10",
"12",
"16",
"18",
"20",
"24",
"26",
"33",
"32",
"36",
"42",
"46",
"48",
"50",
"52",
"53",
"60",
"66",
"68",
"74",
"78",
"82",
"90",
"92",
"97",
"100",
"104",
"106",
"114",
"118",
"120",
"126",
"136",
"140",
"144",
"148",
"150",
"156",
"166",
"170",
"172",
"172",
"176",
"184",
"186",
"198",
"200",
"206",
"214",
"218",
"222",
"226",
"232",
"234",
"246",
"248",
"252",
"256",
"268",
"282"
] | [
"nonn",
"easy",
"nice"
] | 40 | 1 | 1 | [
"A005523",
"A005525"
] | [
"M4067"
] | N. J. A. Sloane | 2024-05-02T04:31:53 | oeisdata/seq/A005/A005525.seq | cd43efd6cd1e21a9edf2bb1c6354ba60 |
A005526 | Maximal number of rational points that a (smooth, geometrically irreducible) curve of genus 3 over the finite field GF(q) can have, where q is the n-th prime power >= 2. | [
"7",
"10",
"14",
"16",
"20",
"24",
"28",
"28",
"32",
"38",
"40",
"44",
"48",
"56",
"56",
"60",
"62",
"64",
"72",
"78",
"80",
"87",
"92",
"96",
"102",
"107",
"113",
"116",
"120",
"122",
"131",
"136",
"136",
"144",
"155"
] | [
"nonn",
"more"
] | 19 | 1 | 1 | [
"A005526",
"A080205"
] | [
"M4338"
] | N. J. A. Sloane. | 2024-05-02T04:31:48 | oeisdata/seq/A005/A005526.seq | 80d2c1e7a78ca3bca89a9389799d3d95 |
A005527 | Maximal number of rational points on a curve of genus n over GF(2). | [
"3",
"5",
"6",
"7",
"8",
"9",
"10",
"10",
"11",
"12",
"13",
"14"
] | [
"nonn",
"more"
] | 25 | 0 | 1 | null | [
"M2388"
] | N. J. A. Sloane. | 2024-05-02T04:31:40 | oeisdata/seq/A005/A005527.seq | 46a97a978a70702e9258be1c467cbc3b |
A005528 | Størmer numbers or arc-cotangent irreducible numbers: numbers k such that the largest prime factor of k^2 + 1 is >= 2*k. | [
"1",
"2",
"4",
"5",
"6",
"9",
"10",
"11",
"12",
"14",
"15",
"16",
"19",
"20",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"33",
"34",
"35",
"36",
"37",
"39",
"40",
"42",
"44",
"45",
"48",
"49",
"51",
"52",
"53",
"54",
"56",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"69",
"71",
"74",
"77",
"78",
"79",
"80",
"81",
"82",
"84",
"85",
"86",
"87",
"88",
"89",
"90",
"92",
"94",
"95",
"96"
] | [
"nonn",
"nice",
"easy"
] | 53 | 1 | 2 | [
"A002312",
"A005528",
"A006530",
"A084925"
] | [
"M0950"
] | N. J. A. Sloane and J. H. Conway | 2025-02-16T08:32:29 | oeisdata/seq/A005/A005528.seq | 7206fba45fc5a2aca2194e10b78d3ab2 |
A005529 | Primitive prime factors of the sequence k^2 + 1 (A002522) in the order that they are found. | [
"2",
"5",
"17",
"13",
"37",
"41",
"101",
"61",
"29",
"197",
"113",
"257",
"181",
"401",
"97",
"53",
"577",
"313",
"677",
"73",
"157",
"421",
"109",
"89",
"613",
"1297",
"137",
"761",
"1601",
"353",
"149",
"1013",
"461",
"1201",
"1301",
"541",
"281",
"2917",
"3137",
"673",
"1741",
"277",
"1861",
"769",
"397",
"241",
"2113",
"4357",
"449",
"2381",
"2521",
"5477"
] | [
"nonn",
"changed"
] | 31 | 1 | 1 | [
"A002312",
"A002313",
"A002522",
"A005528",
"A005529"
] | [
"M1505"
] | N. J. A. Sloane. | 2025-04-27T08:02:11 | oeisdata/seq/A005/A005529.seq | 702597df5c67ce873ab0754ea9f85a93 |
A005530 | Number of Boolean functions of n variables from Post class F(8,inf); number of degenerate Boolean functions of n variables. | [
"2",
"6",
"38",
"942",
"325262",
"25768825638",
"129127208425774833206",
"2722258935367507707190488025630791841374"
] | [
"nonn",
"easy",
"nice"
] | 48 | 1 | 1 | [
"A000371",
"A005530",
"A036239",
"A036240"
] | [
"M1711"
] | N. J. A. Sloane, R. K. Guy | 2017-10-07T02:58:37 | oeisdata/seq/A005/A005530.seq | 08e92ee28017c4b7ec17a166835fd7c3 |
A005531 | Decimal expansion of fifth root of 2. | [
"1",
"1",
"4",
"8",
"6",
"9",
"8",
"3",
"5",
"4",
"9",
"9",
"7",
"0",
"3",
"5",
"0",
"0",
"6",
"7",
"9",
"8",
"6",
"2",
"6",
"9",
"4",
"6",
"7",
"7",
"7",
"9",
"2",
"7",
"5",
"8",
"9",
"4",
"4",
"3",
"8",
"5",
"0",
"8",
"8",
"9",
"0",
"9",
"7",
"7",
"9",
"7",
"5",
"0",
"5",
"5",
"1",
"3",
"7",
"1",
"1",
"1",
"1",
"8",
"4",
"9",
"3",
"6",
"0",
"3",
"2",
"0",
"6",
"2",
"5",
"3",
"5",
"1",
"3",
"0",
"5",
"6",
"8",
"1",
"1",
"4",
"7",
"3",
"1",
"1",
"3",
"0",
"1",
"1",
"5",
"0",
"8",
"4",
"7",
"3",
"9",
"1",
"4",
"5",
"7"
] | [
"nonn",
"cons"
] | 59 | 1 | 3 | [
"A001622",
"A002580",
"A002950",
"A005531",
"A182007",
"A188593"
] | [
"M3321"
] | N. J. A. Sloane | 2025-02-05T11:22:53 | oeisdata/seq/A005/A005531.seq | 5281b13ae99e84aa12207c6a78dcd3c5 |
A005532 | Decimal expansion of fifth root of 3. | [
"1",
"2",
"4",
"5",
"7",
"3",
"0",
"9",
"3",
"9",
"6",
"1",
"5",
"5",
"1",
"7",
"3",
"2",
"5",
"9",
"6",
"6",
"6",
"8",
"0",
"3",
"3",
"6",
"6",
"4",
"0",
"3",
"0",
"5",
"0",
"8",
"0",
"9",
"3",
"9",
"3",
"0",
"9",
"9",
"9",
"3",
"0",
"6",
"8",
"7",
"7",
"9",
"8",
"1",
"1",
"0",
"4",
"6",
"1",
"7",
"3",
"0",
"1",
"4",
"3",
"6",
"0",
"7",
"4",
"6",
"6",
"5",
"3",
"7",
"7",
"5",
"4",
"9",
"3",
"5",
"6",
"6",
"6",
"0",
"5",
"8",
"9",
"5",
"1",
"4",
"4",
"5",
"8",
"8",
"1",
"2",
"3",
"4",
"2",
"5",
"6",
"5",
"9",
"0",
"2"
] | [
"cons",
"nonn"
] | 35 | 1 | 2 | [
"A003117",
"A005532",
"A246708"
] | [
"M0953"
] | N. J. A. Sloane | 2025-02-11T14:41:55 | oeisdata/seq/A005/A005532.seq | b16ce2f742a4d6342b6ac41a8e693b64 |
A005533 | Decimal expansion of fifth root of 4. | [
"1",
"3",
"1",
"9",
"5",
"0",
"7",
"9",
"1",
"0",
"7",
"7",
"2",
"8",
"9",
"4",
"2",
"5",
"9",
"3",
"7",
"4",
"0",
"0",
"1",
"9",
"7",
"1",
"2",
"2",
"9",
"6",
"4",
"0",
"1",
"3",
"3",
"0",
"3",
"3",
"4",
"6",
"9",
"0",
"1",
"3",
"1",
"9",
"3",
"4",
"1",
"8",
"6",
"8",
"1",
"5",
"0",
"5",
"8",
"0",
"7",
"7",
"9",
"5",
"9",
"8",
"0",
"5",
"3",
"5",
"9",
"8",
"0",
"8",
"9",
"3",
"5",
"2",
"0",
"8",
"3",
"0",
"0",
"5",
"0",
"3",
"5"
] | [
"cons",
"nonn"
] | 33 | 1 | 2 | [
"A000120",
"A003118",
"A005533"
] | [
"M2231"
] | N. J. A. Sloane | 2024-02-04T03:23:45 | oeisdata/seq/A005/A005533.seq | 82af2f5fb44b8bb0be7c2954386cbf10 |
A005534 | Decimal expansion of fifth root of 5. | [
"1",
"3",
"7",
"9",
"7",
"2",
"9",
"6",
"6",
"1",
"4",
"6",
"1",
"2",
"1",
"4",
"8",
"3",
"2",
"3",
"9",
"0",
"0",
"6",
"3",
"4",
"6",
"4",
"2",
"1",
"6",
"0",
"1",
"7",
"6",
"9",
"2",
"8",
"5",
"5",
"6",
"4",
"9",
"8",
"7",
"7",
"9",
"7",
"7",
"6",
"0",
"6",
"1",
"2",
"1",
"7",
"7",
"2",
"7",
"3",
"7",
"6",
"7",
"4",
"7",
"9",
"1",
"5",
"0",
"6",
"1",
"8",
"9",
"4",
"2",
"1",
"6",
"3",
"5",
"8",
"3",
"3",
"1",
"5",
"6",
"5",
"8"
] | [
"nonn",
"cons"
] | 36 | 1 | 2 | [
"A002951",
"A005534"
] | [
"M2615"
] | N. J. A. Sloane | 2025-02-05T11:22:57 | oeisdata/seq/A005/A005534.seq | 753feb7ea624c75044f5a765ea4daaae |
A005535 | Number of semi-regular digraphs (with loops) on n unlabeled nodes with each node having out-degree 3. | [
"1",
"19",
"916",
"91212",
"12888450",
"2411213698",
"575737451509",
"171049953499862",
"61944438230597774",
"26879022100485977540",
"13773587720396658214925",
"8231894671550187551622795",
"5676740663627528580559535893",
"4474748487205893704072253926113"
] | [
"nonn",
"nice"
] | 20 | 3 | 2 | [
"A003286",
"A005535",
"A185193",
"A259471"
] | [
"M5081"
] | N. J. A. Sloane | 2022-07-20T07:26:08 | oeisdata/seq/A005/A005535.seq | 766cb54b9c7f1af5b559cb26d0795985 |
A005536 | a(0) = 0; thereafter a(2n) = n - a(n) - a(n-1), a(2n+1) = n - 2a(n) + 1. | [
"0",
"1",
"0",
"0",
"1",
"3",
"3",
"4",
"3",
"3",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"3",
"3",
"4",
"6",
"9",
"10",
"12",
"12",
"13",
"12",
"12",
"13",
"15",
"15",
"16",
"15",
"15",
"13",
"12",
"12",
"13",
"12",
"12",
"10",
"9",
"6",
"4",
"3",
"3",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"3",
"3",
"4",
"3",
"3",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"3",
"3",
"4",
"6",
"9",
"10",
"12",
"12",
"13",
"12",
"12",
"13",
"15",
"15",
"16",
"18",
"21",
"22",
"24",
"27",
"31",
"33"
] | [
"nonn",
"look"
] | 67 | 0 | 6 | [
"A005536",
"A071992",
"A073059"
] | [
"M2274"
] | N. J. A. Sloane | 2024-07-19T08:48:26 | oeisdata/seq/A005/A005536.seq | a87a9676d32d682f603ce1a39ae872be |
A005537 | Numbers m such that 4*3^m + 1 is prime. | [
"0",
"1",
"2",
"3",
"6",
"14",
"15",
"39",
"201",
"249",
"885",
"1005",
"1254",
"1635",
"3306",
"3522",
"9602",
"19785",
"72698",
"233583",
"328689",
"537918",
"887535",
"980925",
"1154598",
"1499606",
"1936890",
"2016951",
"2143374"
] | [
"nonn",
"more"
] | 78 | 1 | 3 | [
"A005537",
"A005540",
"A125734"
] | [
"M0803"
] | N. J. A. Sloane, Chris K. Caldwell | 2024-09-12T11:30:08 | oeisdata/seq/A005/A005537.seq | f112774b77e87eb8fe4df3f49d670b72 |
A005538 | Numbers n such that 8*3^n + 1 is prime. | [
"2",
"7",
"8",
"10",
"22",
"52",
"58",
"76",
"130",
"143",
"331",
"332",
"980",
"1282",
"1655",
"4031",
"4600",
"18880",
"89482",
"130592",
"323860",
"872171",
"1172480"
] | [
"nonn",
"hard"
] | 67 | 1 | 1 | [
"A005538",
"A056799"
] | [
"M1729"
] | N. J. A. Sloane | 2020-07-06T06:05:01 | oeisdata/seq/A005/A005538.seq | 4558747f85c81bd4a1a335a0ea007a74 |
A005539 | Numbers k such that 10*3^k + 1 is prime. | [
"0",
"1",
"3",
"4",
"7",
"9",
"12",
"18",
"22",
"102",
"112",
"157",
"162",
"289",
"619",
"763",
"1389",
"1783",
"1882",
"3294",
"3567",
"13297",
"14932",
"18954",
"19612",
"23598",
"33882",
"66874",
"70546",
"86568",
"187626",
"190738"
] | [
"hard",
"nonn"
] | 33 | 1 | 3 | null | [
"M2337"
] | N. J. A. Sloane | 2022-09-08T08:44:33 | oeisdata/seq/A005/A005539.seq | a4fed439e63b42431d0bd7a8b875e19d |
A005540 | Numbers k such that 4*3^k - 1 is prime. | [
"0",
"1",
"3",
"5",
"7",
"15",
"45",
"95",
"235",
"463",
"733",
"1437",
"1583",
"1677",
"1803",
"4163",
"4765",
"9219",
"9959",
"25477",
"26059",
"41539",
"54195",
"65057",
"74977",
"116589",
"192289",
"311835",
"350767",
"353635",
"416337",
"423253"
] | [
"nonn",
"hard"
] | 31 | 1 | 3 | null | [
"M2422"
] | N. J. A. Sloane | 2018-07-15T12:04:43 | oeisdata/seq/A005/A005540.seq | 80b8c7b6958822dc795bdefbfe8fb075 |
A005541 | Numbers k such that 8*3^k - 1 is prime. | [
"0",
"1",
"2",
"4",
"10",
"17",
"50",
"170",
"184",
"194",
"209",
"641",
"1298",
"4034",
"5956",
"7154",
"9970",
"35956",
"42730",
"132004",
"190610"
] | [
"nonn",
"hard"
] | 41 | 1 | 3 | [
"A001771",
"A002235",
"A003307",
"A005541",
"A046865",
"A046866",
"A046867",
"A056725",
"A079906",
"A079907"
] | [
"M1200"
] | N. J. A. Sloane | 2020-08-01T11:17:19 | oeisdata/seq/A005/A005541.seq | 39e5f6f61414d1156dfabe5a2dc66129 |
A005542 | Numbers k such that 10*3^k - 1 is prime. | [
"1",
"2",
"3",
"4",
"8",
"10",
"14",
"20",
"22",
"26",
"30",
"38",
"39",
"49",
"54",
"58",
"70",
"81",
"84",
"87",
"102",
"111",
"140",
"159",
"207",
"224",
"328",
"358",
"360",
"447",
"484",
"908",
"1083",
"1242",
"1461",
"1705",
"4624",
"5199",
"7106",
"8667",
"11157",
"13130",
"28052",
"30483",
"32166",
"34447",
"36986",
"86578",
"89940",
"120433",
"140743",
"147308",
"159276",
"165543",
"234843",
"437338"
] | [
"hard",
"nonn"
] | 35 | 1 | 2 | null | [
"M0589"
] | N. J. A. Sloane | 2024-10-27T09:27:30 | oeisdata/seq/A005/A005542.seq | 43efd7c9a35e7c37ae8e856e84248b4e |
A005543 | Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,2,2). | [
"1",
"12",
"114",
"940",
"7568",
"61728",
"512996",
"4334884",
"37164700",
"322624804",
"2830973320",
"25074130996",
"223900666504",
"2013718244072"
] | [
"nonn",
"walk"
] | 23 | 2 | 2 | [
"A003287",
"A003288",
"A005543",
"A005544",
"A005545",
"A005546",
"A005547",
"A005548"
] | [
"M4859"
] | N. J. A. Sloane | 2021-12-26T21:19:43 | oeisdata/seq/A005/A005543.seq | efd551f2c3c2ead012d35c8867d69703 |
A005544 | Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (1,1,2). | [
"2",
"18",
"136",
"1030",
"7992",
"63796",
"522474",
"4369840",
"37179840",
"320861342",
"2802304988",
"24725041598",
"220077128644",
"1973963065574"
] | [
"nonn",
"walk"
] | 23 | 2 | 1 | [
"A003287",
"A003288",
"A005543",
"A005544",
"A005545",
"A005546",
"A005547",
"A005548"
] | [
"M2108"
] | N. J. A. Sloane | 2021-12-26T21:19:51 | oeisdata/seq/A005/A005544.seq | a176e83dfcffc6118bd05cad74c119cf |
A005545 | Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,3). | [
"9",
"96",
"835",
"7020",
"58857",
"497360",
"4251804",
"36765592",
"321262541",
"2833702404",
"25204186455",
"225846648440"
] | [
"nonn",
"walk"
] | 19 | 3 | 1 | [
"A003287",
"A003288",
"A005543",
"A005544",
"A005545",
"A005546",
"A005547",
"A005548"
] | [
"M4658"
] | N. J. A. Sloane. | 2016-02-17T15:26:06 | oeisdata/seq/A005/A005545.seq | a44a4c2cabfca0965e168bb88b3b8133 |
A005546 | Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,3,3). | [
"1",
"24",
"360",
"4000",
"39330",
"367912",
"3370604",
"30630980",
"277824572",
"2522478772",
"22959239730",
"209629138108",
"1920548559328"
] | [
"nonn",
"walk"
] | 23 | 3 | 2 | [
"A003287",
"A003288",
"A005543",
"A005544",
"A005545",
"A005546",
"A005547",
"A005548"
] | [
"M5161"
] | N. J. A. Sloane | 2021-12-26T21:20:00 | oeisdata/seq/A005/A005546.seq | a61111cc6f16af61aca1dd221d5d886e |
A005547 | Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (1,2,3). | [
"3",
"52",
"575",
"5470",
"49303",
"436446",
"3850752",
"34063392",
"302790797",
"2706629188",
"24332099665",
"219940720414"
] | [
"nonn",
"walk"
] | 21 | 3 | 1 | [
"A003287",
"A003288",
"A005543",
"A005544",
"A005545",
"A005546",
"A005547",
"A005548"
] | [
"M3158"
] | N. J. A. Sloane | 2022-11-06T19:34:35 | oeisdata/seq/A005/A005547.seq | e6c238814317f9820c907280fc6e1d30 |
A005548 | Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (2,2,2). | [
"6",
"72",
"690",
"6192",
"53946",
"466800",
"4053816",
"35450940",
"312411672",
"2773863060",
"24802293720",
"223203954264",
"2020552369164"
] | [
"nonn",
"walk"
] | 24 | 3 | 1 | [
"A003287",
"A003288",
"A005543",
"A005544",
"A005545",
"A005546",
"A005547",
"A005548"
] | [
"M4277"
] | N. J. A. Sloane | 2021-12-26T21:20:08 | oeisdata/seq/A005/A005548.seq | ba94067fbff3cfbf882f21158e045084 |
A005549 | Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,3). | [
"1",
"12",
"54",
"188",
"636",
"2168",
"7556",
"26826",
"96724",
"353390",
"1305126",
"4864450",
"18272804",
"69103526",
"262871644",
"1005137688",
"3860909698",
"14890903690",
"57641869140",
"223864731680",
"872028568182",
"3406103773674",
"13337263822236"
] | [
"nonn",
"walk",
"more"
] | 23 | 3 | 2 | [
"A001335",
"A003289",
"A003290",
"A003291",
"A005549",
"A005550",
"A005551",
"A005552",
"A005553"
] | [
"M4842"
] | N. J. A. Sloane | 2021-12-26T21:20:30 | oeisdata/seq/A005/A005549.seq | c6f9c8df239e8194c6247d60c8f8011a |
A005550 | Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,2). | [
"3",
"16",
"57",
"184",
"601",
"2036",
"7072",
"25088",
"90503",
"330836",
"1222783",
"4561058",
"17145990",
"64888020",
"246995400",
"944986464",
"3631770111",
"14013725268",
"54268946152",
"210842757798",
"821569514032",
"3209925357702",
"12572219405144"
] | [
"nonn",
"walk",
"more"
] | 22 | 3 | 1 | [
"A001335",
"A003289",
"A003290",
"A003291",
"A005549",
"A005550",
"A005551",
"A005552",
"A005553"
] | [
"M3012"
] | N. J. A. Sloane | 2021-12-26T21:20:38 | oeisdata/seq/A005/A005550.seq | 50a81e42520c07099bb78fbb3c149a8e |
A005551 | Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,4). | [
"1",
"20",
"130",
"576",
"2218",
"8170",
"29830",
"109192",
"402258",
"1492746",
"5578742",
"20986424",
"79420122",
"302175648",
"1155298598",
"4436375790",
"17103294308",
"66174208076",
"256870951048",
"1000080994758",
"3904276709604",
"15280413966512"
] | [
"nonn",
"walk",
"more"
] | 22 | 4 | 2 | [
"A001335",
"A003289",
"A003290",
"A003291",
"A005549",
"A005550",
"A005551",
"A005552",
"A005553"
] | [
"M5090"
] | N. J. A. Sloane | 2021-12-26T21:20:45 | oeisdata/seq/A005/A005551.seq | 681bce853bc823aa16416782e5e08c87 |
A005552 | Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,3). | [
"4",
"35",
"166",
"633",
"2276",
"8107",
"29086",
"105460",
"386320",
"1428664",
"5327738",
"20014741",
"75677726",
"287784832",
"1099944240",
"4223170456",
"16280541834",
"62992268833",
"244536402984",
"952154191644",
"3717618386556",
"14551788319328"
] | [
"nonn",
"walk",
"more"
] | 22 | 4 | 1 | [
"A001335",
"A003289",
"A003290",
"A003291",
"A005549",
"A005550",
"A005551",
"A005552",
"A005553"
] | [
"M3657"
] | N. J. A. Sloane | 2021-12-26T21:20:54 | oeisdata/seq/A005/A005552.seq | b0f2bbc5524641de3259178a2f44b57a |
A005553 | Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (2,2). | [
"6",
"40",
"174",
"644",
"2268",
"8020",
"28666",
"103696",
"379450",
"1402276",
"5227366",
"19633732",
"74230146",
"282273744",
"1078902168",
"4142578832",
"15970882784",
"61798680076",
"239921541412",
"934258870200",
"3648030627298",
"14280474288676"
] | [
"nonn",
"walk",
"more"
] | 23 | 4 | 1 | [
"A001335",
"A003289",
"A003290",
"A003291",
"A005549",
"A005550",
"A005551",
"A005552",
"A005553"
] | [
"M4235"
] | N. J. A. Sloane | 2021-12-26T21:21:06 | oeisdata/seq/A005/A005553.seq | 70a87cf654976433724a1e52afa7a0de |
A005554 | Sums of successive Motzkin numbers. | [
"1",
"2",
"3",
"6",
"13",
"30",
"72",
"178",
"450",
"1158",
"3023",
"7986",
"21309",
"57346",
"155469",
"424206",
"1164039",
"3210246",
"8893161",
"24735666",
"69051303",
"193399578",
"543310782",
"1530523638",
"4322488212",
"12236130298",
"34713220977",
"98677591278"
] | [
"nonn"
] | 66 | 1 | 2 | [
"A001006",
"A005554",
"A014138",
"A059346",
"A080981",
"A102071"
] | [
"M0801"
] | N. J. A. Sloane | 2025-01-19T16:17:34 | oeisdata/seq/A005/A005554.seq | 7f794b80fee585f52c5ab6ef70b404b3 |
A005555 | A finite sequence associated with the Lie algebra E_8. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"20",
"21",
"22",
"24",
"25",
"28",
"29",
"30",
"31",
"32",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"56",
"57",
"60",
"61",
"62",
"63",
"64",
"70",
"84",
"85",
"88",
"110",
"111",
"112",
"120",
"156",
"157",
"159",
"160",
"166",
"182",
"184",
"231",
"232",
"280",
"399",
"400",
"520",
"760",
"1240"
] | [
"nonn",
"fini",
"full"
] | 31 | 0 | 2 | null | null | N. J. A. Sloane | 2022-04-13T13:25:17 | oeisdata/seq/A005/A005555.seq | fcf0bb577b5013301eea25a2fb9c46dc |
A005556 | Exponents m_i associated with Weyl group W(E6). | [
"1",
"4",
"5",
"7",
"8",
"11"
] | [
"nonn",
"fini",
"full"
] | 20 | 1 | 2 | null | null | N. J. A. Sloane | 2022-09-08T08:44:33 | oeisdata/seq/A005/A005556.seq | 18a1e1b2c9775a4f196d7c76142ffc1a |
A005557 | Number of walks on square lattice. | [
"42",
"132",
"297",
"572",
"1001",
"1638",
"2548",
"3808",
"5508",
"7752",
"10659",
"14364",
"19019",
"24794",
"31878",
"40480",
"50830",
"63180",
"77805",
"95004",
"115101",
"138446",
"165416",
"196416",
"231880",
"272272",
"318087",
"369852",
"428127",
"493506",
"566618",
"648128",
"738738",
"839188",
"950257",
"1072764"
] | [
"nonn",
"walk",
"easy"
] | 71 | 0 | 1 | [
"A005557",
"A009766",
"A033184",
"A062991",
"A214292"
] | [
"M5277"
] | N. J. A. Sloane | 2024-02-22T19:15:28 | oeisdata/seq/A005/A005557.seq | 043ed1c229fc7b2c96cac594279707ba |
A005558 | a(n) is the number of n-step walks on square lattice such that 0 <= y <= x at each step. | [
"1",
"1",
"3",
"6",
"20",
"50",
"175",
"490",
"1764",
"5292",
"19404",
"60984",
"226512",
"736164",
"2760615",
"9202050",
"34763300",
"118195220",
"449141836",
"1551580888",
"5924217936",
"20734762776",
"79483257308",
"281248448936",
"1081724803600",
"3863302870000",
"14901311070000",
"53644719852000"
] | [
"nonn",
"walk",
"changed"
] | 167 | 0 | 3 | [
"A000108",
"A000888",
"A000891",
"A005558",
"A005559",
"A005560",
"A005561",
"A005562",
"A005817",
"A052174",
"A093768",
"A138350"
] | [
"M2598"
] | N. J. A. Sloane | 2025-04-19T03:24:31 | oeisdata/seq/A005/A005558.seq | a0983a72fd77c0a8430892295b336734 |
A005559 | Number of walks on square lattice. Column y=1 of A052174. | [
"1",
"2",
"8",
"20",
"75",
"210",
"784",
"2352",
"8820",
"27720",
"104544",
"339768",
"1288287",
"4294290",
"16359200",
"55621280",
"212751396",
"734959368",
"2821056160",
"9873696560",
"38013731756",
"134510127752",
"519227905728",
"1854385377600",
"7174705330000",
"25828939188000",
"100136810390400"
] | [
"nonn",
"walk"
] | 60 | 1 | 2 | [
"A005558",
"A005559",
"A005560",
"A052174",
"A093768"
] | [
"M1832"
] | N. J. A. Sloane | 2025-02-03T11:54:15 | oeisdata/seq/A005/A005559.seq | 38b7e324dbeca49dc5e2ff8e43c2b691 |
A005560 | Number of walks on square lattice. Column y=2 of A052174. | [
"1",
"3",
"15",
"45",
"189",
"588",
"2352",
"7560",
"29700",
"98010",
"382239",
"1288287",
"5010005",
"17177160",
"66745536",
"232092432",
"901995588",
"3173688180",
"12342120700",
"43861998180",
"170724392916",
"611947174608",
"2384209771200",
"8609646396000",
"33577620944400",
"122041737663300",
"476432168185575"
] | [
"nonn",
"walk"
] | 39 | 2 | 2 | [
"A005558",
"A005559",
"A005560",
"A005561",
"A005562",
"A052174",
"A093768"
] | [
"M2987"
] | N. J. A. Sloane | 2025-02-03T11:53:57 | oeisdata/seq/A005/A005560.seq | 51914aa5517b01a8c75fb713c8fda1c3 |
A005561 | Number of walks on square lattice. Column y=3 of A052174. | [
"1",
"4",
"24",
"84",
"392",
"1344",
"5760",
"19800",
"81675",
"283140",
"1145144",
"4008004",
"16032016",
"56632576",
"225059328",
"801773856",
"3173688180",
"11392726800",
"44986664800",
"162594659920",
"641087516256",
"2331227331840",
"9183622822400",
"33577620944400",
"132211882468575",
"485773975404900"
] | [
"nonn",
"walk"
] | 39 | 3 | 2 | [
"A005558",
"A005559",
"A005560",
"A005561",
"A005562",
"A052174",
"A093768"
] | [
"M3596"
] | N. J. A. Sloane | 2025-02-03T11:54:04 | oeisdata/seq/A005/A005561.seq | a68b93098b01086bff15b313ff8d3661 |
A005562 | Number of walks on square lattice. Column y=4 of A052174. | [
"1",
"5",
"35",
"140",
"720",
"2700",
"12375",
"45375",
"196625",
"715715",
"3006003",
"10930920",
"45048640",
"164105760",
"668144880",
"2441298600",
"9859090500",
"36149998500",
"145173803500",
"534239596880",
"2136958387520",
"7892175863000",
"31479019635375",
"116657543354625",
"464342770607625",
"1726402608669375"
] | [
"nonn",
"walk"
] | 49 | 4 | 2 | [
"A005558",
"A005559",
"A005560",
"A005561",
"A005562",
"A052174",
"A093768"
] | [
"M3974"
] | N. J. A. Sloane | 2025-02-03T11:54:10 | oeisdata/seq/A005/A005562.seq | 239d18dda585628b345269592cda740e |
A005563 | a(n) = n*(n+2) = (n+1)^2 - 1. | [
"0",
"3",
"8",
"15",
"24",
"35",
"48",
"63",
"80",
"99",
"120",
"143",
"168",
"195",
"224",
"255",
"288",
"323",
"360",
"399",
"440",
"483",
"528",
"575",
"624",
"675",
"728",
"783",
"840",
"899",
"960",
"1023",
"1088",
"1155",
"1224",
"1295",
"1368",
"1443",
"1520",
"1599",
"1680",
"1763",
"1848",
"1935",
"2024",
"2115",
"2208",
"2303",
"2400",
"2499",
"2600"
] | [
"nonn",
"easy"
] | 527 | 0 | 2 | [
"A000035",
"A000217",
"A000290",
"A000466",
"A001651",
"A002378",
"A005563",
"A007531",
"A008585",
"A008833",
"A013468",
"A016742",
"A019973",
"A028560",
"A033996",
"A046092",
"A053186",
"A054000",
"A055881",
"A056108",
"A062196",
"A067725",
"A067728",
"A067998",
"A068310",
"A069817",
"A079978",
"A080956",
"A085692",
"A102537",
"A120070",
"A120072",
"A123865",
"A123866",
"A123867",
"A123868",
"A134582",
"A140091",
"A140681",
"A143053",
"A144396",
"A156035",
"A163280",
"A212331",
"A253607",
"A367204"
] | [
"M2720"
] | N. J. A. Sloane | 2025-04-02T05:13:08 | oeisdata/seq/A005/A005563.seq | e81ba6aa611fcc5080ff27c6ef531be7 |
A005564 | Number of n-step walks on square lattice in the first quadrant which finish at distance n-3 from the x-axis. | [
"6",
"20",
"45",
"84",
"140",
"216",
"315",
"440",
"594",
"780",
"1001",
"1260",
"1560",
"1904",
"2295",
"2736",
"3230",
"3780",
"4389",
"5060",
"5796",
"6600",
"7475",
"8424",
"9450",
"10556",
"11745",
"13020",
"14384",
"15840",
"17391",
"19040",
"20790",
"22644",
"24605",
"26676",
"28860",
"31160",
"33579",
"36120",
"38786",
"41580",
"44505"
] | [
"nonn",
"walk",
"easy"
] | 128 | 3 | 1 | [
"A000217",
"A001701",
"A005564",
"A093768"
] | [
"M4134"
] | N. J. A. Sloane | 2022-09-08T08:44:33 | oeisdata/seq/A005/A005564.seq | 28eee319f137a9826b3961469dec4aaa |
A005565 | Number of walks on square lattice. | [
"20",
"75",
"189",
"392",
"720",
"1215",
"1925",
"2904",
"4212",
"5915",
"8085",
"10800",
"14144",
"18207",
"23085",
"28880",
"35700",
"43659",
"52877",
"63480",
"75600",
"89375",
"104949",
"122472",
"142100",
"163995",
"188325",
"215264",
"244992",
"277695",
"313565",
"352800",
"395604",
"442187",
"492765",
"547560",
"606800"
] | [
"nonn",
"walk",
"easy"
] | 60 | 0 | 1 | null | [
"M5087"
] | N. J. A. Sloane | 2022-09-08T08:44:33 | oeisdata/seq/A005/A005565.seq | cf5816e66eae229bccd666b4f72a8e17 |
A005566 | Number of walks of length n on square lattice, starting at origin, staying in first quadrant. | [
"1",
"2",
"6",
"18",
"60",
"200",
"700",
"2450",
"8820",
"31752",
"116424",
"426888",
"1585584",
"5889312",
"22084920",
"82818450",
"312869700",
"1181952200",
"4491418360",
"17067389768",
"65166397296",
"248817153312",
"953799087696",
"3656229836168",
"14062422446800",
"54086240180000",
"208618354980000"
] | [
"nonn",
"walk",
"changed"
] | 91 | 0 | 2 | [
"A000894",
"A001700",
"A005566",
"A060150",
"A060897",
"A060900"
] | [
"M1627"
] | N. J. A. Sloane | 2025-04-19T04:29:20 | oeisdata/seq/A005/A005566.seq | 6f51a0817fdf34276f4f1ac37012961b |
A005567 | Number of walks on square lattice. | [
"10",
"70",
"308",
"1092",
"3414",
"9834",
"26752",
"69784",
"176306",
"434382",
"1048812",
"2490636",
"5833006",
"13500754",
"30933368",
"70255008",
"158335434",
"354419190",
"788529700",
"1744831060",
"3841983110",
"8422163130",
"18387829488"
] | [
"nonn",
"walk",
"easy"
] | 41 | 0 | 1 | null | [
"M4723"
] | N. J. A. Sloane | 2022-04-13T13:25:17 | oeisdata/seq/A005/A005567.seq | 9b898bdaeb83b31ca96fed9348f6dc43 |
A005568 | Product of two successive Catalan numbers C(n)*C(n+1). | [
"1",
"2",
"10",
"70",
"588",
"5544",
"56628",
"613470",
"6952660",
"81662152",
"987369656",
"12228193432",
"154532114800",
"1986841476000",
"25928281261800",
"342787130211150",
"4583937702039300",
"61923368957373000",
"844113292629453000",
"11600528392993339800",
"160599522947154548400",
"2238236829690383152800"
] | [
"nonn",
"easy"
] | 189 | 0 | 2 | [
"A000108",
"A000356",
"A004304",
"A005568",
"A005817",
"A168450",
"A168451",
"A168452"
] | [
"M1972"
] | R. K. Guy, Simon Plouffe and N. J. A. Sloane | 2024-05-03T17:11:54 | oeisdata/seq/A005/A005568.seq | 9e204b2954dd4ff570637e618f384850 |
A005569 | Number of walks on square lattice. | [
"4",
"34",
"308",
"3024",
"31680",
"349206",
"4008004",
"47530912",
"579058896",
"7215393640",
"91644262864",
"1183274479040",
"15497363512800",
"205519758825150",
"2755739674246500",
"37314861293793600",
"509727100259638800"
] | [
"nonn",
"walk",
"easy"
] | 32 | 1 | 1 | null | [
"M3654"
] | N. J. A. Sloane | 2018-04-11T02:56:29 | oeisdata/seq/A005/A005569.seq | 537db6d58ed7278201871a3de4ac662b |
A005570 | Number of walks on cubic lattice. | [
"17",
"50",
"99",
"164",
"245",
"342",
"455",
"584",
"729",
"890",
"1067",
"1260",
"1469",
"1694",
"1935",
"2192",
"2465",
"2754",
"3059",
"3380",
"3717",
"4070",
"4439",
"4824",
"5225",
"5642",
"6075",
"6524",
"6989",
"7470",
"7967",
"8480",
"9009",
"9554",
"10115",
"10692",
"11285",
"11894",
"12519",
"13160",
"13817",
"14490",
"15179",
"15884",
"16605"
] | [
"nonn",
"walk",
"easy"
] | 72 | 1 | 1 | [
"A000217",
"A001620",
"A005570",
"A158057",
"A250129"
] | [
"M5038"
] | N. J. A. Sloane | 2025-01-28T15:28:27 | oeisdata/seq/A005/A005570.seq | 0a1ec400df24b553da44fe7b1f2da36e |
A005571 | Number of walks on cubic lattice. | [
"76",
"288",
"700",
"1376",
"2380",
"3776",
"5628",
"8000",
"10956",
"14560",
"18876",
"23968",
"29900",
"36736",
"44540",
"53376",
"63308",
"74400",
"86716",
"100320",
"115276",
"131648",
"149500",
"168896",
"189900",
"212576",
"236988",
"263200",
"291276",
"321280",
"353276",
"387328",
"423500",
"461856",
"502460",
"545376"
] | [
"nonn",
"walk",
"easy"
] | 47 | 0 | 1 | null | [
"M5352"
] | N. J. A. Sloane | 2022-09-10T07:34:44 | oeisdata/seq/A005/A005571.seq | 98bf6a156b1e542984071fab80d8995e |
A005572 | Number of walks on cubic lattice starting and finishing on the xy plane and never going below it. | [
"1",
"4",
"17",
"76",
"354",
"1704",
"8421",
"42508",
"218318",
"1137400",
"5996938",
"31940792",
"171605956",
"928931280",
"5061593709",
"27739833228",
"152809506582",
"845646470616",
"4699126915422",
"26209721959656",
"146681521121244",
"823429928805936"
] | [
"nonn",
"walk",
"easy",
"nice"
] | 204 | 0 | 2 | [
"A001006",
"A002212",
"A005572",
"A025228",
"A025230",
"A108198",
"A129400",
"A182401"
] | [
"M3539"
] | N. J. A. Sloane | 2025-01-19T14:42:45 | oeisdata/seq/A005/A005572.seq | 52efc667bd03325d5029d5fe9111d109 |
A005573 | Number of walks on cubic lattice (starting from origin and not going below xy plane). | [
"1",
"5",
"26",
"139",
"758",
"4194",
"23460",
"132339",
"751526",
"4290838",
"24607628",
"141648830",
"817952188",
"4736107172",
"27487711752",
"159864676803",
"931448227590",
"5435879858958",
"31769632683132",
"185918669183370",
"1089302293140564"
] | [
"nonn",
"walk",
"easy",
"nice"
] | 96 | 0 | 2 | null | [
"M3943"
] | N. J. A. Sloane | 2025-01-19T14:42:05 | oeisdata/seq/A005/A005573.seq | 7e64cc69fe7b38dfd98057583874e69b |
A005574 | Numbers k such that k^2 + 1 is prime. | [
"1",
"2",
"4",
"6",
"10",
"14",
"16",
"20",
"24",
"26",
"36",
"40",
"54",
"56",
"66",
"74",
"84",
"90",
"94",
"110",
"116",
"120",
"124",
"126",
"130",
"134",
"146",
"150",
"156",
"160",
"170",
"176",
"180",
"184",
"204",
"206",
"210",
"224",
"230",
"236",
"240",
"250",
"256",
"260",
"264",
"270",
"280",
"284",
"300",
"306",
"314",
"326",
"340",
"350",
"384",
"386",
"396"
] | [
"nonn",
"easy",
"nice",
"changed"
] | 136 | 1 | 2 | [
"A000068",
"A001912",
"A002496",
"A002522",
"A005574",
"A006313",
"A006314",
"A006315",
"A006316",
"A007591",
"A010051",
"A049422",
"A056994",
"A056995",
"A057002",
"A057465",
"A062325",
"A067201",
"A078402",
"A088361",
"A088362",
"A090693",
"A114269",
"A114270",
"A114271",
"A114272",
"A114273",
"A114274",
"A114275",
"A226528",
"A226529",
"A226530",
"A243959",
"A244150",
"A251597",
"A253854",
"A259645",
"A295405",
"A321323"
] | [
"M1010"
] | N. J. A. Sloane | 2025-04-23T23:32:42 | oeisdata/seq/A005/A005574.seq | 64331fc3fbdb283a77137b118008dd7c |
A005575 | a(n) = A259095(2n,n). | [
"0",
"0",
"1",
"2",
"5",
"11",
"20",
"37",
"63",
"110",
"174",
"283",
"435",
"671",
"1001",
"1492",
"2160",
"3127",
"4442",
"6269",
"8739",
"12109",
"16597",
"22618",
"30576",
"41077",
"54834",
"72788",
"96056",
"126131",
"164829",
"214327",
"277534",
"357810",
"459507",
"587779",
"749220",
"951473",
"1204501",
"1519691",
"1911618",
"2397247",
"2997985",
"3738482",
"4649981",
"5768457",
"7138640",
"8812704",
"10854735",
"13339286"
] | [
"nonn",
"nice"
] | 33 | 1 | 4 | [
"A005575",
"A005576",
"A005577",
"A259095"
] | [
"M1390"
] | N. J. A. Sloane, R. K. Guy | 2016-07-28T05:23:10 | oeisdata/seq/A005/A005575.seq | 14c0a0390de1475b922f985fb7791eb0 |
A005576 | The limiting sequence [A259095(r(r+1)/2-s,r), s=0,1,2,...,r-1] for very large r. | [
"1",
"1",
"2",
"3",
"4",
"7",
"9",
"13",
"17",
"25",
"32",
"43",
"56",
"73",
"95",
"122",
"155",
"196",
"248",
"309",
"388",
"480",
"595",
"731",
"899",
"1096",
"1338",
"1624",
"1967",
"2373",
"2860",
"3431",
"4111",
"4911",
"5853",
"6963",
"8263",
"9785",
"11565",
"13646",
"16064",
"18884",
"22155",
"25953",
"30349",
"35441",
"41311",
"48098",
"55906",
"64900",
"75231",
"87103",
"100702",
"116296",
"134130",
"154522"
] | [
"nonn",
"nice"
] | 45 | 0 | 3 | [
"A005575",
"A005576",
"A005577",
"A259095"
] | [
"M0583"
] | N. J. A. Sloane, R. K. Guy | 2023-10-29T21:12:01 | oeisdata/seq/A005/A005576.seq | 69cb7b98d4ab82bfc35ca60636b09cc5 |
A005577 | Maxima of the rows of the triangle A259095. | [
"1",
"1",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"9",
"11",
"15",
"20",
"27",
"35",
"44",
"56",
"73",
"91",
"115",
"148",
"186",
"227",
"283",
"358",
"435",
"538",
"671",
"813",
"1001",
"1233",
"1492",
"1815",
"2223",
"2673",
"3247",
"3933",
"4713",
"5683",
"6850",
"8170",
"9785",
"11725",
"13948",
"16587",
"19783",
"23468",
"27710",
"32942",
"38956",
"45852",
"54133",
"63879",
"75000",
"87909",
"103471",
"121273",
"141629"
] | [
"nonn",
"nice"
] | 41 | 1 | 4 | [
"A005575",
"A005576",
"A005577",
"A259095"
] | [
"M0495"
] | N. J. A. Sloane, R. K. Guy | 2023-10-29T21:12:26 | oeisdata/seq/A005/A005577.seq | ae26ea42d8dc33b21177c386ff6f1495 |
A005578 | a(2*n) = 2*a(2*n-1), a(2*n+1) = 2*a(2*n)-1. | [
"1",
"1",
"2",
"3",
"6",
"11",
"22",
"43",
"86",
"171",
"342",
"683",
"1366",
"2731",
"5462",
"10923",
"21846",
"43691",
"87382",
"174763",
"349526",
"699051",
"1398102",
"2796203",
"5592406",
"11184811",
"22369622",
"44739243",
"89478486",
"178956971",
"357913942",
"715827883",
"1431655766",
"2863311531",
"5726623062",
"11453246123"
] | [
"easy",
"nonn"
] | 215 | 0 | 3 | [
"A000975",
"A001045",
"A005578",
"A006356",
"A007583",
"A047849",
"A071922",
"A072176",
"A129761",
"A135229"
] | [
"M0788"
] | N. J. A. Sloane | 2025-02-16T08:32:29 | oeisdata/seq/A005/A005578.seq | b890a81bc1374c13ecd44e5b075d67a8 |
A005579 | a(n) = smallest number k such that Product_{i=1..k} prime(i)/(prime(i)-1) > n. | [
"0",
"1",
"2",
"3",
"4",
"6",
"9",
"14",
"22",
"35",
"55",
"89",
"142",
"230",
"373",
"609",
"996",
"1637",
"2698",
"4461",
"7398",
"12301",
"20503",
"34253",
"57348",
"96198",
"161659",
"272124",
"458789",
"774616",
"1309627",
"2216968",
"3757384",
"6375166",
"10828012",
"18409028",
"31326514",
"53354259",
"90945529",
"155142139"
] | [
"nonn",
"changed"
] | 61 | 0 | 3 | [
"A000720",
"A001611",
"A005579",
"A005580",
"A023199",
"A038110",
"A060753",
"A072986",
"A091440",
"A256968"
] | [
"M0573"
] | N. J. A. Sloane, R. K. Guy | 2025-04-18T09:57:29 | oeisdata/seq/A005/A005579.seq | 0493202c722d2ee14b2ead45c93415af |
A005580 | a(n) = smallest number k such that Product_{i=2..k+1} prime(i)/(prime(i)-1) > n. | [
"0",
"1",
"3",
"8",
"21",
"54",
"141",
"372",
"995",
"2697",
"7397",
"20502",
"57347",
"161658",
"458788",
"1309626",
"3757383",
"10828011",
"31326513",
"90945528"
] | [
"nonn",
"more"
] | 33 | 0 | 3 | [
"A005579",
"A005580"
] | [
"M2740"
] | N. J. A. Sloane. | 2025-01-31T09:52:07 | oeisdata/seq/A005/A005580.seq | 4fe691f8db307b4280702ffc1565c1ff |
A005581 | a(n) = (n-1)*n*(n+4)/6. | [
"0",
"0",
"2",
"7",
"16",
"30",
"50",
"77",
"112",
"156",
"210",
"275",
"352",
"442",
"546",
"665",
"800",
"952",
"1122",
"1311",
"1520",
"1750",
"2002",
"2277",
"2576",
"2900",
"3250",
"3627",
"4032",
"4466",
"4930",
"5425",
"5952",
"6512",
"7106",
"7735",
"8400",
"9102",
"9842",
"10621",
"11440",
"12300",
"13202",
"14147",
"15136",
"16170"
] | [
"nonn",
"easy",
"nice"
] | 168 | 0 | 3 | [
"A000211",
"A000217",
"A000292",
"A005581",
"A005582",
"A005586",
"A052928",
"A111808",
"A127672",
"A128209",
"A176222"
] | [
"M1744"
] | N. J. A. Sloane | 2025-02-16T08:32:29 | oeisdata/seq/A005/A005581.seq | 577dadd552797663159d3730fd3b21e1 |
A005582 | a(n) = n*(n+1)*(n+2)*(n+7)/24. | [
"0",
"2",
"9",
"25",
"55",
"105",
"182",
"294",
"450",
"660",
"935",
"1287",
"1729",
"2275",
"2940",
"3740",
"4692",
"5814",
"7125",
"8645",
"10395",
"12397",
"14674",
"17250",
"20150",
"23400",
"27027",
"31059",
"35525",
"40455",
"45880",
"51832",
"58344",
"65450",
"73185",
"81585",
"90687",
"100529",
"111150",
"122590",
"134890"
] | [
"nonn",
"easy"
] | 108 | 0 | 2 | [
"A000211",
"A005581",
"A005582",
"A052928",
"A128209",
"A176222"
] | [
"M1922"
] | N. J. A. Sloane | 2025-01-05T19:51:33 | oeisdata/seq/A005/A005582.seq | 0f931a71f83e02e64fb91dc78d0d7a8a |
A005583 | Coefficients of Chebyshev polynomials. | [
"2",
"11",
"36",
"91",
"196",
"378",
"672",
"1122",
"1782",
"2717",
"4004",
"5733",
"8008",
"10948",
"14688",
"19380",
"25194",
"32319",
"40964",
"51359",
"63756",
"78430",
"95680",
"115830",
"139230",
"166257",
"197316",
"232841",
"273296",
"319176",
"371008",
"429352",
"494802",
"567987",
"649572",
"740259",
"840788"
] | [
"nonn",
"easy"
] | 92 | 1 | 1 | [
"A000096",
"A000217",
"A000389",
"A005583",
"A051747",
"A127672",
"A207606"
] | [
"M1999"
] | N. J. A. Sloane | 2023-02-17T10:04:04 | oeisdata/seq/A005/A005583.seq | 0a365eb280330580d086d64188c0dff0 |
A005584 | Coefficients of Chebyshev polynomials. | [
"2",
"13",
"49",
"140",
"336",
"714",
"1386",
"2508",
"4290",
"7007",
"11011",
"16744",
"24752",
"35700",
"50388",
"69768",
"94962",
"127281",
"168245",
"219604",
"283360",
"361790",
"457470",
"573300",
"712530",
"878787",
"1076103",
"1308944",
"1582240",
"1901416",
"2272424",
"2701776",
"3196578",
"3764565",
"4414137",
"5154396"
] | [
"nonn",
"easy"
] | 69 | 1 | 1 | [
"A005581",
"A005582",
"A005583",
"A005584",
"A127672"
] | [
"M2059"
] | N. J. A. Sloane | 2023-02-17T08:15:26 | oeisdata/seq/A005/A005584.seq | 5f1c04b7bf041588c8d14446b1b91ea3 |
A005585 | 5-dimensional pyramidal numbers: a(n) = n*(n+1)*(n+2)*(n+3)*(2n+3)/5!. | [
"1",
"7",
"27",
"77",
"182",
"378",
"714",
"1254",
"2079",
"3289",
"5005",
"7371",
"10556",
"14756",
"20196",
"27132",
"35853",
"46683",
"59983",
"76153",
"95634",
"118910",
"146510",
"179010",
"217035",
"261261",
"312417",
"371287",
"438712",
"515592",
"602888",
"701624",
"812889",
"937839",
"1077699",
"1233765",
"1407406"
] | [
"nonn",
"easy"
] | 167 | 1 | 2 | [
"A000389",
"A002415",
"A005585",
"A006542",
"A027800",
"A034263",
"A040977",
"A047819",
"A051836",
"A051843",
"A051877",
"A051878",
"A051879",
"A053120",
"A084960",
"A111125"
] | [
"M4387"
] | N. J. A. Sloane | 2025-01-07T15:56:17 | oeisdata/seq/A005/A005585.seq | 80e74b04c14d1288e879fdb0a05ee113 |
A005586 | a(n) = n*(n+4)*(n+5)/6. | [
"0",
"5",
"14",
"28",
"48",
"75",
"110",
"154",
"208",
"273",
"350",
"440",
"544",
"663",
"798",
"950",
"1120",
"1309",
"1518",
"1748",
"2000",
"2275",
"2574",
"2898",
"3248",
"3625",
"4030",
"4464",
"4928",
"5423",
"5950",
"6510",
"7104",
"7733",
"8398",
"9100",
"9840",
"10619",
"11438",
"12298",
"13200",
"14145",
"15134",
"16168",
"17248"
] | [
"nonn",
"easy"
] | 83 | 0 | 2 | [
"A000217",
"A000292",
"A005581",
"A005586",
"A009766",
"A053121"
] | [
"M3841"
] | N. J. A. Sloane | 2024-11-22T09:35:58 | oeisdata/seq/A005/A005586.seq | 38de44cdafbe18f6be6546c893ca7171 |
A005587 | a(n) = n*(n+5)*(n+6)*(n+7)/24. | [
"0",
"14",
"42",
"90",
"165",
"275",
"429",
"637",
"910",
"1260",
"1700",
"2244",
"2907",
"3705",
"4655",
"5775",
"7084",
"8602",
"10350",
"12350",
"14625",
"17199",
"20097",
"23345",
"26970",
"31000",
"35464",
"40392",
"45815",
"51765",
"58275",
"65379",
"73112",
"81510",
"90610",
"100450",
"111069",
"122507",
"134805",
"148005"
] | [
"nonn",
"easy"
] | 77 | 0 | 2 | [
"A005587",
"A009766",
"A033184",
"A062991"
] | [
"M4929"
] | N. J. A. Sloane | 2024-11-22T09:15:22 | oeisdata/seq/A005/A005587.seq | 39c85a81bd4e8fe23c367aed8dc0281a |
A005588 | Number of free binary trees admitting height n. | [
"2",
"7",
"52",
"2133",
"2590407",
"3374951541062",
"5695183504479116640376509",
"16217557574922386301420514191523784895639577710480",
"131504586847961235687181874578063117114329409897550318273792033024340388219235081096658023517076950"
] | [
"nonn",
"easy",
"core",
"nice"
] | 68 | 1 | 1 | [
"A002658",
"A005588",
"A006894"
] | [
"M1813"
] | N. J. A. Sloane; entry revised by N. J. A. Sloane, Aug 31 2012 | 2022-08-28T08:22:55 | oeisdata/seq/A005/A005588.seq | 5a5b8d8fb603e8bc6b5675d851eada95 |
A005589 | Number of letters in the US English name of n, excluding spaces and hyphens. | [
"4",
"3",
"3",
"5",
"4",
"4",
"3",
"5",
"5",
"4",
"3",
"6",
"6",
"8",
"8",
"7",
"7",
"9",
"8",
"8",
"6",
"9",
"9",
"11",
"10",
"10",
"9",
"11",
"11",
"10",
"6",
"9",
"9",
"11",
"10",
"10",
"9",
"11",
"11",
"10",
"5",
"8",
"8",
"10",
"9",
"9",
"8",
"10",
"10",
"9",
"5",
"8",
"8",
"10",
"9",
"9",
"8",
"10",
"10",
"9",
"5",
"8",
"8",
"10",
"9",
"9",
"8",
"10",
"10",
"9",
"7",
"10",
"10",
"12",
"11",
"11",
"10",
"12",
"12",
"11",
"6",
"9",
"9",
"11",
"10",
"10",
"9",
"11",
"11",
"10",
"6",
"9",
"9",
"11",
"10",
"10",
"9",
"11",
"11",
"10",
"10",
"13",
"13",
"15",
"14",
"14",
"13",
"15",
"15",
"14",
"13",
"16",
"16",
"18",
"18",
"17",
"17",
"19",
"18",
"18",
"16"
] | [
"nonn",
"word",
"nice"
] | 122 | 0 | 1 | [
"A005589",
"A006944",
"A007208",
"A016037",
"A052360",
"A052362",
"A052363",
"A133418",
"A134629",
"A362123"
] | [
"M2277"
] | N. J. A. Sloane | 2025-02-16T08:32:29 | oeisdata/seq/A005/A005589.seq | f627efe68fb85506838a9410898e7146 |
A005590 | a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n+1) - a(n). | [
"0",
"1",
"1",
"0",
"1",
"-1",
"0",
"1",
"1",
"-2",
"-1",
"1",
"0",
"1",
"1",
"0",
"1",
"-3",
"-2",
"1",
"-1",
"2",
"1",
"-1",
"0",
"1",
"1",
"0",
"1",
"-1",
"0",
"1",
"1",
"-4",
"-3",
"1",
"-2",
"3",
"1",
"-2",
"-1",
"3",
"2",
"-1",
"1",
"-2",
"-1",
"1",
"0",
"1",
"1",
"0",
"1",
"-1",
"0",
"1",
"1",
"-2",
"-1",
"1",
"0",
"1",
"1",
"0",
"1",
"-5",
"-4",
"1",
"-3",
"4",
"1",
"-3",
"-2",
"5",
"3",
"-2",
"1",
"-3",
"-2",
"1",
"-1",
"4",
"3",
"-1",
"2",
"-3",
"-1",
"2",
"1",
"-3",
"-2",
"1",
"-1",
"2",
"1",
"-1",
"0",
"1",
"1",
"0",
"1",
"-1",
"0",
"1",
"1"
] | [
"sign",
"nice",
"easy",
"look"
] | 96 | 0 | 10 | [
"A002487",
"A005590",
"A182093"
] | [
"M0048"
] | N. J. A. Sloane | 2025-03-28T17:32:25 | oeisdata/seq/A005/A005590.seq | f2b8a0085a3bb45ae86fc4e78928b8b0 |
A005591 | Number of semigroups of order n with 3 idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator). | [
"6",
"44",
"351",
"3093",
"33445",
"600027",
"68769167",
"219587421825"
] | [
"nonn"
] | 21 | 3 | 1 | [
"A005591",
"A058123"
] | [
"M4246"
] | N. J. A. Sloane | 2018-11-08T14:39:36 | oeisdata/seq/A005/A005591.seq | 9f5f22145d1b438dbbb5e7b1337e9d95 |
A005592 | a(n) = F(2n+1) + F(2n-1) - 1. | [
"1",
"2",
"6",
"17",
"46",
"122",
"321",
"842",
"2206",
"5777",
"15126",
"39602",
"103681",
"271442",
"710646",
"1860497",
"4870846",
"12752042",
"33385281",
"87403802",
"228826126",
"599074577",
"1568397606",
"4106118242",
"10749957121",
"28143753122",
"73681302246",
"192900153617",
"505019158606",
"1322157322202"
] | [
"nonn",
"easy",
"nice"
] | 125 | 0 | 2 | [
"A000032",
"A000045",
"A002878",
"A004146",
"A005248",
"A005592",
"A014217",
"A065034"
] | [
"M1619"
] | N. J. A. Sloane | 2025-01-05T19:51:33 | oeisdata/seq/A005/A005592.seq | 3b318ca2be62781ef87708b4cc4b3381 |
A005593 | a(n) = (F(2n+1) + F(2n-1) + F(n+3) - 2)/2, where F() = Fibonacci numbers A000045. | [
"2",
"5",
"12",
"29",
"71",
"177",
"448",
"1147",
"2960",
"7679",
"19989",
"52145",
"136214",
"356121",
"931540",
"2437513",
"6379403",
"16698113",
"43710756",
"114427391",
"299560472",
"784236315",
"2053119817",
"5375076769",
"14072035466",
"36840908237",
"96450492828",
"252510252437"
] | [
"nonn",
"easy"
] | 27 | 1 | 1 | null | [
"M1414"
] | N. J. A. Sloane | 2022-04-13T13:25:17 | oeisdata/seq/A005/A005593.seq | e8cd8112181aa42de6eacceb7b02ee37 |
A005594 | States of a dynamic storage system. | [
"1",
"2",
"4",
"7",
"14",
"26",
"59",
"122",
"284",
"647",
"1528",
"3602",
"8679",
"20882",
"50824",
"124055",
"304574",
"750122",
"1855099",
"4600202",
"11442086",
"28527447",
"71292604",
"178526882",
"447919419",
"1125750146",
"2833906684",
"7144450567",
"18036423974"
] | [
"nonn"
] | 29 | 0 | 2 | [
"A005594",
"A032198"
] | [
"M1080"
] | N. J. A. Sloane | 2019-11-08T03:42:47 | oeisdata/seq/A005/A005594.seq | 496f4dadf13bc3e941eff08f5652e484 |
A005595 | States of a dynamic storage system. | [
"1",
"2",
"4",
"7",
"13",
"23",
"46",
"88",
"186",
"395",
"880",
"1989",
"4644",
"10934",
"26210",
"63319",
"154377",
"378443",
"933022",
"2308956",
"5735371",
"14286907",
"35683814",
"89324137",
"224057918",
"563033978",
"1417210456",
"3572641303",
"9018885121",
"22796905055",
"57692673962",
"146167385344",
"370710166434"
] | [
"nonn"
] | 28 | 0 | 2 | null | [
"M1069"
] | N. J. A. Sloane | 2018-06-21T03:05:47 | oeisdata/seq/A005/A005595.seq | 64d54130a7d3aa928321f6a9014047ad |
A005596 | Decimal expansion of Artin's constant Product_{p=prime} (1-1/(p^2-p)). | [
"3",
"7",
"3",
"9",
"5",
"5",
"8",
"1",
"3",
"6",
"1",
"9",
"2",
"0",
"2",
"2",
"8",
"8",
"0",
"5",
"4",
"7",
"2",
"8",
"0",
"5",
"4",
"3",
"4",
"6",
"4",
"1",
"6",
"4",
"1",
"5",
"1",
"1",
"1",
"6",
"2",
"9",
"2",
"4",
"8",
"6",
"0",
"6",
"1",
"5",
"0",
"0",
"4",
"2",
"0",
"9",
"4",
"7",
"4",
"2",
"8",
"0",
"2",
"4",
"1",
"7",
"3",
"5",
"0",
"1",
"8",
"2",
"0",
"4",
"0",
"0",
"2",
"8",
"0",
"8",
"2",
"3",
"4",
"4",
"3",
"0",
"4",
"3",
"1",
"7",
"0",
"8",
"7",
"2",
"5",
"0",
"5",
"6",
"8",
"9",
"8",
"1",
"6",
"0",
"3"
] | [
"nonn",
"cons"
] | 112 | 0 | 1 | [
"A001122",
"A001913",
"A005596",
"A048296",
"A065414"
] | [
"M2608"
] | N. J. A. Sloane | 2025-03-15T14:44:23 | oeisdata/seq/A005/A005596.seq | 99e37b104447e41f77dfd068b58a3abf |
A005597 | Decimal expansion of the twin prime constant C_2 = Product_{ p prime >= 3 } (1-1/(p-1)^2). | [
"6",
"6",
"0",
"1",
"6",
"1",
"8",
"1",
"5",
"8",
"4",
"6",
"8",
"6",
"9",
"5",
"7",
"3",
"9",
"2",
"7",
"8",
"1",
"2",
"1",
"1",
"0",
"0",
"1",
"4",
"5",
"5",
"5",
"7",
"7",
"8",
"4",
"3",
"2",
"6",
"2",
"3",
"3",
"6",
"0",
"2",
"8",
"4",
"7",
"3",
"3",
"4",
"1",
"3",
"3",
"1",
"9",
"4",
"4",
"8",
"4",
"2",
"3",
"3",
"3",
"5",
"4",
"0",
"5",
"6",
"4",
"2",
"3",
"0",
"4",
"4",
"9",
"5",
"2",
"7",
"7",
"1",
"4",
"3",
"7",
"6",
"0",
"0",
"3",
"1",
"4",
"1",
"3",
"8",
"3",
"9",
"8",
"6",
"7",
"9",
"1",
"1",
"7",
"7",
"9"
] | [
"cons",
"nonn",
"nice",
"changed"
] | 126 | 0 | 1 | [
"A000010",
"A005597",
"A008683",
"A062270",
"A062271",
"A065418",
"A065645",
"A065646",
"A065647",
"A114907",
"A167864"
] | [
"M4056"
] | N. J. A. Sloane | 2025-04-25T12:53:23 | oeisdata/seq/A005/A005597.seq | 0d52d058c14322f59c3454c64a5476e7 |
A005598 | a(n) = 1 + Sum_{i=1..n} (n-i+1)*phi(i). | [
"1",
"2",
"4",
"8",
"14",
"24",
"36",
"54",
"76",
"104",
"136",
"178",
"224",
"282",
"346",
"418",
"498",
"594",
"696",
"816",
"944",
"1084",
"1234",
"1406",
"1586",
"1786",
"1998",
"2228",
"2470",
"2740",
"3018",
"3326",
"3650",
"3994",
"4354",
"4738",
"5134",
"5566",
"6016",
"6490",
"6980",
"7510",
"8052",
"8636",
"9240",
"9868",
"10518",
"11214"
] | [
"nonn",
"nice"
] | 65 | 0 | 2 | [
"A000010",
"A002088",
"A005598",
"A011755",
"A049695",
"A049703",
"A103116"
] | [
"M1097"
] | N. J. A. Sloane | 2023-01-24T07:51:00 | oeisdata/seq/A005/A005598.seq | f9d61f7927083254c4bc9455cf3f20b9 |
A005599 | Running sum of every third term in the {+1,-1}-version of Thue-Morse sequence A010060. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"11",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"18",
"19",
"20",
"21",
"20",
"19",
"18",
"19",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"29",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"35",
"36",
"35",
"34",
"33",
"34",
"35",
"36",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"42",
"43",
"44",
"45",
"46",
"47",
"48",
"47",
"48",
"49",
"50"
] | [
"nonn",
"easy",
"nice"
] | 63 | 0 | 3 | [
"A000120",
"A005599",
"A010060",
"A106400"
] | [
"M0468"
] | M. R. Schroeder | 2024-05-23T11:56:22 | oeisdata/seq/A005/A005599.seq | 0892fb5ce5f3666271987cac0672e839 |
A005600 | Decimal expansion of reciprocal of fine-structure constant alpha. | [
"1",
"3",
"7",
"0",
"3",
"5",
"9",
"9",
"9"
] | [
"cons",
"nonn"
] | 74 | 3 | 2 | [
"A003673",
"A005600",
"A082726"
] | [
"M2606"
] | N. J. A. Sloane, Mira Bernstein | 2022-10-13T22:31:48 | oeisdata/seq/A005/A005600.seq | 60b63d3182b83c9bb8ced233e7fdd599 |
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