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666,262,453B
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listlengths 1
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listlengths 1
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timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A001601 | a(n) = 2*a(n-1)^2 - 1, if n>1. a(0)=1, a(1)=3. | [
"1",
"3",
"17",
"577",
"665857",
"886731088897",
"1572584048032918633353217",
"4946041176255201878775086487573351061418968498177"
]
| [
"nonn",
"easy",
"nice",
"frac"
]
| 117 | 0 | 2 | [
"A001333",
"A001601",
"A003423",
"A051009"
]
| [
"M3042",
"N1234"
]
| N. J. A. Sloane | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001601.seq | f36f2bce084a53e82242a80855666072 |
A001602 | Fibonacci entry points: a(n) = smallest m > 0 such that the n-th prime divides Fibonacci(m). | [
"3",
"4",
"5",
"8",
"10",
"7",
"9",
"18",
"24",
"14",
"30",
"19",
"20",
"44",
"16",
"27",
"58",
"15",
"68",
"70",
"37",
"78",
"84",
"11",
"49",
"50",
"104",
"36",
"27",
"19",
"128",
"130",
"69",
"46",
"37",
"50",
"79",
"164",
"168",
"87",
"178",
"90",
"190",
"97",
"99",
"22",
"42",
"224",
"228",
"114",
"13",
"238",
"120",
"250",
"129",
"88",
"67",
"270",
"139",
"28",
"284",
"147",
"44",
"310"
]
| [
"nonn",
"nice"
]
| 163 | 1 | 1 | [
"A001177",
"A001602",
"A051694",
"A086597",
"A194363"
]
| [
"M2310",
"N0912"
]
| N. J. A. Sloane | 2025-04-21T23:26:29 | oeisdata/seq/A001/A001602.seq | 02a8ab68c86b2ca33172fc45174d452a |
A001603 | Odd-indexed terms of A124296. | [
"1",
"11",
"101",
"781",
"5611",
"39161",
"270281",
"1857451",
"12744061",
"87382901",
"599019851",
"4105974961",
"28143378001",
"192899171531",
"1322154751061",
"9062194370461",
"62113232767531",
"425730505493801",
"2918000490238361",
"20000273409331051",
"137083914639998701",
"939587132382262661"
]
| [
"nonn",
"easy"
]
| 48 | 0 | 2 | [
"A001603",
"A001604",
"A124296",
"A124297"
]
| [
"M4801",
"N2051"
]
| N. J. A. Sloane | 2023-06-25T02:37:26 | oeisdata/seq/A001/A001603.seq | 09c06b27070b0b9ace2d2f9060c7a5e8 |
A001604 | Odd-indexed terms of A124297. | [
"11",
"31",
"151",
"911",
"5951",
"40051",
"272611",
"1863551",
"12760031",
"87424711",
"599129311",
"4106261531",
"28144128251",
"192901135711",
"1322159893351",
"9062207833151",
"62113268013311",
"425730597768451",
"2918000731816531",
"20000274041790911",
"137083916295800111",
"939587136717207031",
"6440026032054760351"
]
| [
"nonn",
"easy"
]
| 51 | 0 | 1 | [
"A001603",
"A001604",
"A124296",
"A124297"
]
| [
"M4785",
"N2042"
]
| N. J. A. Sloane | 2023-06-25T02:38:55 | oeisdata/seq/A001/A001604.seq | 42c42f67ca7590ec88054d147adc62e2 |
A001605 | Indices of prime Fibonacci numbers. | [
"3",
"4",
"5",
"7",
"11",
"13",
"17",
"23",
"29",
"43",
"47",
"83",
"131",
"137",
"359",
"431",
"433",
"449",
"509",
"569",
"571",
"2971",
"4723",
"5387",
"9311",
"9677",
"14431",
"25561",
"30757",
"35999",
"37511",
"50833",
"81839",
"104911",
"130021",
"148091",
"201107",
"397379",
"433781",
"590041",
"593689",
"604711",
"931517",
"1049897",
"1285607",
"1636007",
"1803059",
"1968721",
"2904353",
"3244369",
"3340367"
]
| [
"nonn",
"hard",
"nice"
]
| 187 | 1 | 1 | [
"A000045",
"A001578",
"A001605",
"A005478",
"A046022",
"A080345",
"A086597",
"A117595",
"A303215"
]
| [
"M2309",
"N0911"
]
| N. J. A. Sloane | 2025-07-02T01:07:09 | oeisdata/seq/A001/A001605.seq | 48f0c72380f171b5c48ccdf357806188 |
A001606 | Indices of prime Lucas numbers. | [
"0",
"2",
"4",
"5",
"7",
"8",
"11",
"13",
"16",
"17",
"19",
"31",
"37",
"41",
"47",
"53",
"61",
"71",
"79",
"113",
"313",
"353",
"503",
"613",
"617",
"863",
"1097",
"1361",
"4787",
"4793",
"5851",
"7741",
"8467",
"10691",
"12251",
"13963",
"14449",
"19469",
"35449",
"36779",
"44507",
"51169",
"56003",
"81671",
"89849",
"94823",
"140057",
"148091",
"159521",
"183089",
"193201",
"202667",
"344293",
"387433",
"443609",
"532277",
"574219",
"616787",
"631181",
"637751",
"651821",
"692147",
"901657",
"1051849"
]
| [
"nonn",
"hard",
"nice"
]
| 97 | 1 | 2 | [
"A000032",
"A000204",
"A001605",
"A001606",
"A005479",
"A076697",
"A080327"
]
| [
"M0961",
"N0358"
]
| N. J. A. Sloane | 2025-04-25T10:28:11 | oeisdata/seq/A001/A001606.seq | 95352245abe6ddb0272b37769fc75988 |
A001607 | a(n) = -a(n-1) - 2*a(n-2). | [
"0",
"1",
"-1",
"-1",
"3",
"-1",
"-5",
"7",
"3",
"-17",
"11",
"23",
"-45",
"-1",
"91",
"-89",
"-93",
"271",
"-85",
"-457",
"627",
"287",
"-1541",
"967",
"2115",
"-4049",
"-181",
"8279",
"-7917",
"-8641",
"24475",
"-7193",
"-41757",
"56143",
"27371",
"-139657",
"84915",
"194399",
"-364229",
"-24569",
"753027",
"-703889"
]
| [
"sign",
"easy"
]
| 96 | 0 | 5 | [
"A001607",
"A002249",
"A077020",
"A077021",
"A107920",
"A167433",
"A169998",
"A172250"
]
| [
"M2225",
"N0883"
]
| N. J. A. Sloane | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001607.seq | 66af75842e113f1ab46f69a1a18591d6 |
A001608 | Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2. | [
"3",
"0",
"2",
"3",
"2",
"5",
"5",
"7",
"10",
"12",
"17",
"22",
"29",
"39",
"51",
"68",
"90",
"119",
"158",
"209",
"277",
"367",
"486",
"644",
"853",
"1130",
"1497",
"1983",
"2627",
"3480",
"4610",
"6107",
"8090",
"10717",
"14197",
"18807",
"24914",
"33004",
"43721",
"57918",
"76725",
"101639",
"134643",
"178364",
"236282",
"313007",
"414646",
"549289"
]
| [
"nonn",
"easy",
"nice"
]
| 457 | 0 | 1 | [
"A000931",
"A001608",
"A013998",
"A018187",
"A109377",
"A182097"
]
| [
"M0429",
"N0163"
]
| N. J. A. Sloane | 2025-05-29T11:10:06 | oeisdata/seq/A001/A001608.seq | 70b377f8767bf8d7fe5418654b7e8d07 |
A001609 | a(1) = a(2) = 1, a(3) = 4; thereafter a(n) = a(n-1) + a(n-3). | [
"1",
"1",
"4",
"5",
"6",
"10",
"15",
"21",
"31",
"46",
"67",
"98",
"144",
"211",
"309",
"453",
"664",
"973",
"1426",
"2090",
"3063",
"4489",
"6579",
"9642",
"14131",
"20710",
"30352",
"44483",
"65193",
"95545",
"140028",
"205221",
"300766",
"440794",
"646015",
"946781",
"1387575",
"2033590",
"2980371",
"4367946",
"6401536",
"9381907"
]
| [
"nonn",
"easy"
]
| 99 | 1 | 3 | [
"A000079",
"A000204",
"A000930",
"A001609",
"A003269",
"A003520",
"A005708",
"A005709",
"A005710",
"A014097",
"A049064",
"A049194",
"A218439"
]
| [
"M3240",
"N1308"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001609.seq | 64f0f41f816205f4e503b1b9888d5d34 |
A001610 | a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 2. | [
"0",
"2",
"3",
"6",
"10",
"17",
"28",
"46",
"75",
"122",
"198",
"321",
"520",
"842",
"1363",
"2206",
"3570",
"5777",
"9348",
"15126",
"24475",
"39602",
"64078",
"103681",
"167760",
"271442",
"439203",
"710646",
"1149850",
"1860497",
"3010348",
"4870846",
"7881195",
"12752042",
"20633238",
"33385281",
"54018520"
]
| [
"nonn",
"easy",
"hear",
"changed"
]
| 174 | 0 | 2 | [
"A000032",
"A000071",
"A000126",
"A000204",
"A000296",
"A001610",
"A001644",
"A032190",
"A169985",
"A174625",
"A306357"
]
| [
"M0764",
"N0291"
]
| N. J. A. Sloane | 2025-07-09T11:09:22 | oeisdata/seq/A001/A001610.seq | f70db022d804b7a5560942a63b30baf3 |
A001611 | a(n) = Fibonacci(n) + 1. | [
"1",
"2",
"2",
"3",
"4",
"6",
"9",
"14",
"22",
"35",
"56",
"90",
"145",
"234",
"378",
"611",
"988",
"1598",
"2585",
"4182",
"6766",
"10947",
"17712",
"28658",
"46369",
"75026",
"121394",
"196419",
"317812",
"514230",
"832041",
"1346270",
"2178310",
"3524579",
"5702888",
"9227466",
"14930353",
"24157818",
"39088170",
"63245987",
"102334156"
]
| [
"nonn",
"easy",
"hear"
]
| 140 | 0 | 2 | [
"A000045",
"A000071",
"A001611",
"A001911",
"A002062",
"A006327",
"A019863",
"A097280",
"A097281",
"A157725",
"A157726",
"A157727",
"A157728",
"A157729",
"A160536",
"A167616",
"A212272",
"A242876"
]
| [
"M0288",
"N0103"
]
| N. J. A. Sloane | 2024-11-28T11:11:53 | oeisdata/seq/A001/A001611.seq | 06556c3486cdde457541693607518e44 |
A001612 | a(n) = a(n-1) + a(n-2) - 1 for n > 1, a(0)=3, a(1)=2. | [
"3",
"2",
"4",
"5",
"8",
"12",
"19",
"30",
"48",
"77",
"124",
"200",
"323",
"522",
"844",
"1365",
"2208",
"3572",
"5779",
"9350",
"15128",
"24477",
"39604",
"64080",
"103683",
"167762",
"271444",
"439205",
"710648",
"1149852",
"1860499",
"3010350",
"4870848",
"7881197",
"12752044",
"20633240",
"33385283",
"54018522"
]
| [
"nonn",
"easy",
"hear"
]
| 113 | 0 | 1 | [
"A000032",
"A000071",
"A001612",
"A274017"
]
| [
"M0974",
"N0364"
]
| N. J. A. Sloane | 2025-06-01T03:16:45 | oeisdata/seq/A001/A001612.seq | 8e15154ab9ed018aaa2f1fe65c060ddc |
A001613 | Delete all odd digits from n. | [
"0",
"0",
"2",
"0",
"4",
"0",
"6",
"0",
"8",
"0",
"0",
"0",
"2",
"0",
"4",
"0",
"6",
"0",
"8",
"0",
"20",
"2",
"22",
"2",
"24",
"2",
"26",
"2",
"28",
"2",
"0",
"0",
"2",
"0",
"4",
"0",
"6",
"0",
"8",
"0",
"40",
"4",
"42",
"4",
"44",
"4",
"46",
"4",
"48",
"4",
"0",
"0",
"2",
"0",
"4",
"0",
"6",
"0",
"8",
"0",
"60",
"6",
"62",
"6",
"64",
"6",
"66",
"6",
"68",
"6",
"0",
"0",
"2",
"0",
"4",
"0",
"6",
"0",
"8",
"0",
"80",
"8"
]
| [
"base",
"nonn"
]
| 8 | 0 | 3 | null | null | N. J. A. Sloane | 2022-02-01T23:33:50 | oeisdata/seq/A001/A001613.seq | fad2302dc79a77a3aac1c1336acc4f93 |
A001614 | Connell sequence: 1 odd, 2 even, 3 odd, ... | [
"1",
"2",
"4",
"5",
"7",
"9",
"10",
"12",
"14",
"16",
"17",
"19",
"21",
"23",
"25",
"26",
"28",
"30",
"32",
"34",
"36",
"37",
"39",
"41",
"43",
"45",
"47",
"49",
"50",
"52",
"54",
"56",
"58",
"60",
"62",
"64",
"65",
"67",
"69",
"71",
"73",
"75",
"77",
"79",
"81",
"82",
"84",
"86",
"88",
"90",
"92",
"94",
"96",
"98",
"100",
"101",
"103",
"105",
"107",
"109",
"111",
"113",
"115",
"117",
"119",
"121",
"122"
]
| [
"nonn",
"easy",
"nice",
"tabl"
]
| 105 | 1 | 2 | [
"A000290",
"A000292",
"A001614",
"A002522",
"A008865",
"A014132",
"A023531",
"A028347",
"A028878",
"A028884",
"A054569",
"A057211",
"A058187",
"A069778",
"A117384",
"A117619",
"A117950",
"A117951",
"A118011",
"A118012",
"A154533",
"A190716",
"A190717",
"A190718"
]
| [
"M0962",
"N0359"
]
| N. J. A. Sloane | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001614.seq | d5ca0b8342b978e07b3321c79f41e5ad |
A001615 | Dedekind psi function: n * Product_{p|n, p prime} (1 + 1/p). | [
"1",
"3",
"4",
"6",
"6",
"12",
"8",
"12",
"12",
"18",
"12",
"24",
"14",
"24",
"24",
"24",
"18",
"36",
"20",
"36",
"32",
"36",
"24",
"48",
"30",
"42",
"36",
"48",
"30",
"72",
"32",
"48",
"48",
"54",
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"72",
"38",
"60",
"56",
"72",
"42",
"96",
"44",
"72",
"72",
"72",
"48",
"96",
"56",
"90",
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"84",
"54",
"108",
"72",
"96",
"80",
"90",
"60",
"144",
"62",
"96",
"96",
"96",
"84",
"144",
"68",
"108",
"96"
]
| [
"nonn",
"easy",
"core",
"nice",
"mult"
]
| 293 | 1 | 2 | [
"A000082",
"A000203",
"A001615",
"A002110",
"A003050",
"A003051",
"A019269",
"A027748",
"A033196",
"A034444",
"A054345",
"A063659",
"A065958",
"A065959",
"A065960",
"A082020",
"A082695",
"A124010",
"A156303",
"A160889",
"A160891",
"A173290",
"A175732",
"A175836",
"A203444",
"A210523",
"A291784",
"A301594",
"A339925",
"A344695",
"A351300",
"A351301",
"A351302",
"A351303",
"A351304",
"A351305"
]
| [
"M2315",
"N0915"
]
| N. J. A. Sloane | 2025-03-30T14:17:06 | oeisdata/seq/A001/A001615.seq | 9ed2e4158919b20609cf6749b8d070c9 |
A001616 | Number of parabolic vertices of Gamma_0(n). | [
"1",
"2",
"2",
"3",
"2",
"4",
"2",
"4",
"4",
"4",
"2",
"6",
"2",
"4",
"4",
"6",
"2",
"8",
"2",
"6",
"4",
"4",
"2",
"8",
"6",
"4",
"6",
"6",
"2",
"8",
"2",
"8",
"4",
"4",
"4",
"12",
"2",
"4",
"4",
"8",
"2",
"8",
"2",
"6",
"8",
"4",
"2",
"12",
"8",
"12",
"4",
"6",
"2",
"12",
"4",
"8",
"4",
"4",
"2",
"12",
"2",
"4",
"8",
"12",
"4",
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"2",
"6",
"4",
"8",
"2",
"16",
"2",
"4",
"12",
"6",
"4",
"8",
"2",
"12",
"12",
"4",
"2",
"12",
"4",
"4",
"4",
"8",
"2",
"16",
"4",
"6",
"4",
"4",
"4",
"16"
]
| [
"nonn",
"easy",
"nice",
"mult"
]
| 71 | 1 | 2 | [
"A000010",
"A001616",
"A027748",
"A027750",
"A124010"
]
| [
"M0247",
"N0087"
]
| N. J. A. Sloane | 2024-07-06T01:34:00 | oeisdata/seq/A001/A001616.seq | b3c2067b25a87b431c2a66fe3696fd39 |
A001617 | Genus of modular group Gamma_0(n). Or, genus of modular curve X_0(n). | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"2",
"2",
"1",
"0",
"2",
"1",
"2",
"2",
"3",
"2",
"1",
"3",
"3",
"3",
"1",
"2",
"4",
"3",
"3",
"3",
"5",
"3",
"4",
"3",
"5",
"4",
"3",
"1",
"2",
"5",
"5",
"4",
"4",
"5",
"5",
"5",
"6",
"5",
"7",
"4",
"7",
"5",
"3",
"5",
"9",
"5",
"7",
"7",
"9",
"6",
"5",
"5",
"8",
"5",
"8",
"7",
"11",
"6",
"7",
"4",
"9",
"7",
"11",
"7",
"10",
"9",
"9",
"7",
"11",
"7",
"10",
"9",
"11",
"9",
"9",
"7",
"7",
"9",
"7",
"8",
"15"
]
| [
"nonn",
"easy",
"nice"
]
| 75 | 1 | 22 | [
"A000086",
"A000089",
"A001615",
"A001616",
"A001617",
"A054728",
"A091401",
"A091403",
"A091404"
]
| [
"M0188",
"N0069"
]
| N. J. A. Sloane | 2023-10-27T19:22:42 | oeisdata/seq/A001/A001617.seq | 720fd884ee4eeb3a855fc1869890b00b |
A001618 | Nearest integer to 2*n*log(n). | [
"0",
"0",
"3",
"7",
"11",
"16",
"22",
"27",
"33",
"40",
"46",
"53",
"60",
"67",
"74",
"81",
"89",
"96",
"104",
"112",
"120",
"128",
"136",
"144",
"153",
"161",
"169",
"178",
"187",
"195",
"204",
"213",
"222",
"231",
"240",
"249",
"258",
"267",
"276",
"286",
"295",
"305",
"314",
"323",
"333",
"343",
"352",
"362",
"372",
"381",
"391",
"401",
"411",
"421",
"431",
"441"
]
| [
"nonn",
"easy"
]
| 31 | 0 | 3 | null | [
"M2623",
"N1038"
]
| N. J. A. Sloane | 2025-01-23T16:53:00 | oeisdata/seq/A001/A001618.seq | 25dbad7fda3ae73e8235c1f88769b40d |
A001619 | Number of letters in English name for n increases at these numbers. | [
"1",
"3",
"11",
"13",
"17",
"21",
"23",
"73",
"101",
"103",
"111",
"113",
"117",
"121",
"123",
"173",
"323",
"373",
"1103",
"1111",
"1113",
"1117",
"1121",
"1123",
"1173",
"1323",
"1373",
"3323",
"3373",
"11373",
"13323",
"13373",
"17373",
"21373",
"23323",
"23373",
"73373",
"101173",
"101323",
"101373",
"103323",
"103373"
]
| [
"word",
"nonn"
]
| 10 | 1 | 2 | null | null | N. J. A. Sloane | 2022-02-01T23:34:09 | oeisdata/seq/A001/A001619.seq | 895303f466effd6b501d2d62a605c41b |
A001620 | Decimal expansion of Euler's constant (or the Euler-Mascheroni constant), gamma. | [
"5",
"7",
"7",
"2",
"1",
"5",
"6",
"6",
"4",
"9",
"0",
"1",
"5",
"3",
"2",
"8",
"6",
"0",
"6",
"0",
"6",
"5",
"1",
"2",
"0",
"9",
"0",
"0",
"8",
"2",
"4",
"0",
"2",
"4",
"3",
"1",
"0",
"4",
"2",
"1",
"5",
"9",
"3",
"3",
"5",
"9",
"3",
"9",
"9",
"2",
"3",
"5",
"9",
"8",
"8",
"0",
"5",
"7",
"6",
"7",
"2",
"3",
"4",
"8",
"8",
"4",
"8",
"6",
"7",
"7",
"2",
"6",
"7",
"7",
"7",
"6",
"6",
"4",
"6",
"7",
"0",
"9",
"3",
"6",
"9",
"4",
"7",
"0",
"6",
"3",
"2",
"9",
"1",
"7",
"4",
"6",
"7",
"4",
"9"
]
| [
"nonn",
"cons",
"nice",
"changed"
]
| 457 | 0 | 1 | [
"A001620",
"A002852",
"A073004",
"A075266",
"A082633",
"A086279",
"A086280",
"A086281",
"A086282",
"A094640",
"A183141",
"A183167",
"A183206",
"A184853",
"A184854",
"A199332",
"A231095",
"A252898",
"A262235",
"A262382",
"A262383",
"A262384",
"A262385",
"A262386",
"A262387",
"A301816",
"A301817"
]
| [
"M3755",
"N1532"
]
| N. J. A. Sloane | 2025-07-08T11:04:19 | oeisdata/seq/A001/A001620.seq | 6ba42d42e148d67e8374578bcc12db2a |
A001621 | a(n) = n*(n + 1)*(n^2 + n + 2)/4. | [
"0",
"2",
"12",
"42",
"110",
"240",
"462",
"812",
"1332",
"2070",
"3080",
"4422",
"6162",
"8372",
"11130",
"14520",
"18632",
"23562",
"29412",
"36290",
"44310",
"53592",
"64262",
"76452",
"90300",
"105950",
"123552",
"143262",
"165242",
"189660",
"216690",
"246512",
"279312",
"315282",
"354620",
"397530",
"444222",
"494912",
"549822"
]
| [
"nonn",
"easy"
]
| 40 | 0 | 2 | [
"A000124",
"A000217",
"A001621",
"A002817",
"A034262",
"A058919",
"A092365"
]
| null | N. J. A. Sloane | 2022-10-08T16:39:33 | oeisdata/seq/A001/A001621.seq | fd03941a3138800275cd257f04ca8e74 |
A001622 | Decimal expansion of golden ratio phi (or tau) = (1 + sqrt(5))/2. | [
"1",
"6",
"1",
"8",
"0",
"3",
"3",
"9",
"8",
"8",
"7",
"4",
"9",
"8",
"9",
"4",
"8",
"4",
"8",
"2",
"0",
"4",
"5",
"8",
"6",
"8",
"3",
"4",
"3",
"6",
"5",
"6",
"3",
"8",
"1",
"1",
"7",
"7",
"2",
"0",
"3",
"0",
"9",
"1",
"7",
"9",
"8",
"0",
"5",
"7",
"6",
"2",
"8",
"6",
"2",
"1",
"3",
"5",
"4",
"4",
"8",
"6",
"2",
"2",
"7",
"0",
"5",
"2",
"6",
"0",
"4",
"6",
"2",
"8",
"1",
"8",
"9",
"0",
"2",
"4",
"4",
"9",
"7",
"0",
"7",
"2",
"0",
"7",
"2",
"0",
"4",
"1",
"8",
"9",
"3",
"9",
"1",
"1",
"3",
"7",
"4",
"8",
"4",
"7",
"5"
]
| [
"nonn",
"cons",
"core",
"nice",
"easy"
]
| 590 | 1 | 2 | [
"A000012",
"A000032",
"A000045",
"A001622",
"A002163",
"A006497",
"A080039",
"A094874",
"A102208",
"A102769",
"A104457",
"A131595",
"A134973",
"A139339",
"A145996",
"A188635",
"A192222",
"A192223",
"A197762",
"A302973",
"A303069",
"A304022"
]
| [
"M4046",
"N1679"
]
| N. J. A. Sloane | 2025-06-08T16:17:06 | oeisdata/seq/A001/A001622.seq | ea2fb7172af1c4e3956984607418f4a8 |
A001623 | Number of 3 X n reduced (normalized) Latin rectangles. | [
"1",
"4",
"46",
"1064",
"35792",
"1673792",
"103443808",
"8154999232",
"798030483328",
"94866122760704",
"13460459852344064",
"2246551018310998016",
"435626600453967929344",
"97108406689489312301056",
"24658059294992101453262848",
"7075100096781964808223653888",
"2277710095706779480096994066432",
"817555425148510266964075644059648"
]
| [
"nonn",
"nice"
]
| 51 | 3 | 2 | [
"A001009",
"A001623"
]
| [
"M3682",
"N1502"
]
| N. J. A. Sloane | 2016-11-09T15:03:10 | oeisdata/seq/A001/A001623.seq | 39c53fad201ce5c46130a2862bf2bddd |
A001624 | Related to Latin rectangles. | [
"1",
"5",
"58",
"1274",
"41728",
"1912112",
"116346400",
"9059742176",
"877746364288",
"103483282967936",
"14581464284095744",
"2419278174185319680",
"466730664414683625472",
"103580258158369503481856",
"26198788829773597178540032"
]
| [
"nonn"
]
| 20 | 2 | 2 | null | [
"M4017",
"N1665"
]
| N. J. A. Sloane | 2022-02-01T23:34:22 | oeisdata/seq/A001/A001624.seq | 111c3e1876571bde7bada00180e8f3b8 |
A001625 | Related to Latin rectangles. | [
"2",
"4",
"60",
"1276",
"41888",
"1916064",
"116522048",
"9069595840",
"878460379392",
"103547791177216",
"14588580791234048",
"2420219602973093376",
"466877775127725240320",
"103607067936116866084864",
"26204424894484840874483712"
]
| [
"nonn"
]
| 20 | 2 | 1 | null | [
"M1304",
"N0500"
]
| N. J. A. Sloane | 2022-02-01T23:36:20 | oeisdata/seq/A001/A001625.seq | e18eebecc39bc4c5950a1b70f9ac4e0d |
A001626 | Number of 3-line Latin rectangles. | [
"0",
"0",
"2",
"36",
"840",
"29680",
"1429920",
"90318144",
"7237943552",
"717442928640",
"86171602072320",
"12331048749268480",
"2072725870491859968",
"404352831489304049664",
"90605920564322676531200",
"23110943021722435879157760",
"6657484407493222296916131840"
]
| [
"nonn"
]
| 23 | 1 | 3 | [
"A000186",
"A001626"
]
| [
"M2158",
"N0860"
]
| N. J. A. Sloane | 2022-02-01T23:36:40 | oeisdata/seq/A001/A001626.seq | 591301c4e0a37d76746dad0bbb845845 |
A001627 | Related to Latin rectangles. | [
"1",
"0",
"2",
"44",
"1008",
"34432",
"1629280",
"101401344",
"8030787968",
"788377273856",
"93933191303424",
"13350759115563520",
"2231133728986759168",
"433075048506207645696",
"96617322164029448916992",
"24549315871469898190266368",
"7047652261245574026565877760"
]
| [
"nonn"
]
| 18 | 1 | 3 | null | [
"M2165",
"N0862"
]
| N. J. A. Sloane | 2022-02-01T23:36:59 | oeisdata/seq/A001/A001627.seq | b8565adc4c7398f36a3f7b14acb9a516 |
A001628 | Convolved Fibonacci numbers. | [
"1",
"3",
"9",
"22",
"51",
"111",
"233",
"474",
"942",
"1836",
"3522",
"6666",
"12473",
"23109",
"42447",
"77378",
"140109",
"252177",
"451441",
"804228",
"1426380",
"2519640",
"4434420",
"7777860",
"13599505",
"23709783",
"41225349",
"71501422",
"123723351",
"213619683",
"368080793",
"633011454",
"1086665562",
"1862264196"
]
| [
"nonn",
"easy"
]
| 154 | 0 | 2 | [
"A001628",
"A037027",
"A055243",
"A291915"
]
| [
"M2789",
"N1124"
]
| N. J. A. Sloane, Simon Plouffe | 2025-05-07T09:03:30 | oeisdata/seq/A001/A001628.seq | 1aab44ee530d0819a061bb7384fec4f3 |
A001629 | Self-convolution of Fibonacci numbers. | [
"0",
"0",
"1",
"2",
"5",
"10",
"20",
"38",
"71",
"130",
"235",
"420",
"744",
"1308",
"2285",
"3970",
"6865",
"11822",
"20284",
"34690",
"59155",
"100610",
"170711",
"289032",
"488400",
"823800",
"1387225",
"2332418",
"3916061",
"6566290",
"10996580",
"18394910",
"30737759",
"51310978",
"85573315",
"142587180",
"237387960",
"394905492"
]
| [
"nonn",
"easy",
"nice"
]
| 407 | 0 | 4 | [
"A000032",
"A000045",
"A001628",
"A001629",
"A006478",
"A010049",
"A037027",
"A055244",
"A058071",
"A134510",
"A134836",
"A214178"
]
| [
"M1377",
"N0537"
]
| N. J. A. Sloane | 2025-05-15T00:43:10 | oeisdata/seq/A001/A001629.seq | 4f3be1f52df2f24221edb3204e87c75a |
A001630 | Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0)=a(1)=0, a(2)=1, a(3)=2. | [
"0",
"0",
"1",
"2",
"3",
"6",
"12",
"23",
"44",
"85",
"164",
"316",
"609",
"1174",
"2263",
"4362",
"8408",
"16207",
"31240",
"60217",
"116072",
"223736",
"431265",
"831290",
"1602363",
"3088654",
"5953572",
"11475879",
"22120468",
"42638573",
"82188492",
"158423412",
"305370945",
"588621422",
"1134604271",
"2187020050"
]
| [
"nonn",
"easy"
]
| 110 | 0 | 4 | [
"A000032",
"A001630",
"A007283",
"A054886",
"A078042",
"A096231",
"A163876",
"A179070",
"A265057",
"A265058",
"A265059",
"A265060",
"A265061",
"A265062",
"A265063",
"A265064",
"A265065",
"A265066",
"A265067",
"A265068",
"A265069",
"A265070",
"A265071",
"A265072",
"A265073",
"A265074",
"A265075",
"A265076",
"A265077"
]
| [
"M0795",
"N0301"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001630.seq | 745d0b8d6ebc170c4608f3fd9fa2b487 |
A001631 | Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4), with initial conditions a(0..3) = (0, 0, 1, 0). | [
"0",
"0",
"1",
"0",
"1",
"2",
"4",
"7",
"14",
"27",
"52",
"100",
"193",
"372",
"717",
"1382",
"2664",
"5135",
"9898",
"19079",
"36776",
"70888",
"136641",
"263384",
"507689",
"978602",
"1886316",
"3635991",
"7008598",
"13509507",
"26040412",
"50194508",
"96753025",
"186497452",
"359485397",
"692930382",
"1335666256",
"2574579487"
]
| [
"nonn",
"easy"
]
| 119 | 0 | 6 | [
"A000078",
"A000288",
"A000336",
"A001631"
]
| [
"M1081",
"N0410"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001631.seq | f5b35c1d1b43e12a685c88fbe0192912 |
A001632 | Smallest prime p such that there is a gap of 2n between p and previous prime. | [
"5",
"11",
"29",
"97",
"149",
"211",
"127",
"1847",
"541",
"907",
"1151",
"1693",
"2503",
"2999",
"4327",
"5623",
"1361",
"9587",
"30631",
"19373",
"16183",
"15727",
"81509",
"28277",
"31957",
"19661",
"35671",
"82129",
"44351",
"43391",
"34123",
"89753",
"162209",
"134581",
"173429",
"31469",
"404671",
"212777"
]
| [
"nonn",
"nice",
"easy"
]
| 38 | 1 | 1 | [
"A000230",
"A001632",
"A002386"
]
| [
"M3812",
"N1560"
]
| N. J. A. Sloane | 2021-12-19T10:02:50 | oeisdata/seq/A001/A001632.seq | 111310f669e479eb57c8ff017cafc037 |
A001633 | Numbers with an odd number of digits. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"100",
"101",
"102",
"103",
"104",
"105",
"106",
"107",
"108",
"109",
"110",
"111",
"112",
"113",
"114",
"115",
"116",
"117",
"118",
"119",
"120",
"121",
"122",
"123",
"124",
"125",
"126",
"127",
"128",
"129",
"130",
"131",
"132",
"133",
"134",
"135",
"136",
"137",
"138",
"139",
"140",
"141",
"142",
"143",
"144",
"145"
]
| [
"nonn",
"base",
"easy"
]
| 30 | 1 | 3 | [
"A001633",
"A001637",
"A055642"
]
| null | N. J. A. Sloane | 2022-11-29T12:24:51 | oeisdata/seq/A001/A001633.seq | 3b435dd0dd09b7ff0213fbb82adcf687 |
A001634 | a(n) = a(n-2) + a(n-3) + a(n-4), with initial values a(0) = 0, a(1) = 2, a(2) = 3, a(3) = 6. | [
"0",
"2",
"3",
"6",
"5",
"11",
"14",
"22",
"30",
"47",
"66",
"99",
"143",
"212",
"308",
"454",
"663",
"974",
"1425",
"2091",
"3062",
"4490",
"6578",
"9643",
"14130",
"20711",
"30351",
"44484",
"65192",
"95546",
"140027",
"205222",
"300765",
"440795",
"646014",
"946782",
"1387574",
"2033591",
"2980370",
"4367947",
"6401535",
"9381908"
]
| [
"nonn",
"easy",
"nice"
]
| 58 | 0 | 2 | [
"A001634",
"A013979",
"A107458"
]
| [
"M0746",
"N0281"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001634.seq | 9e8ece60d08067733ead2f704c08f14c |
A001635 | A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-6), n >= 7. | [
"0",
"2",
"3",
"6",
"10",
"11",
"21",
"30",
"48",
"72",
"110",
"171",
"260",
"401",
"613",
"942",
"1445",
"2216",
"3401",
"5216",
"8004",
"12278",
"18837",
"28899",
"44335",
"68018",
"104349",
"160089",
"245601",
"376791",
"578057",
"886830",
"1360538",
"2087279",
"3202216",
"4912704",
"7536863",
"11562737",
"17739062",
"27214520"
]
| [
"nonn"
]
| 55 | 1 | 2 | [
"A000129",
"A001635"
]
| [
"M0762",
"N0289"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001635.seq | 4f019f64a24236b8dd78d75fc85bbbf7 |
A001636 | A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-7), n >= 8. | [
"0",
"2",
"3",
"6",
"10",
"17",
"21",
"38",
"57",
"92",
"143",
"225",
"351",
"555",
"868",
"1366",
"2142",
"3365",
"5282",
"8296",
"13023",
"20451",
"32108",
"50417",
"79160",
"124295",
"195159",
"306431",
"481139",
"755462",
"1186184",
"1862486",
"2924375",
"4591702",
"7209646",
"11320209",
"17774393",
"27908418",
"43820325"
]
| [
"nonn"
]
| 45 | 1 | 2 | [
"A001636",
"A013983"
]
| [
"M0763",
"N0290"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001636.seq | 7baa54f46e95b239d100bee3775a05c6 |
A001637 | Numbers with an even number of digits. | [
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"76",
"77",
"78",
"79",
"80",
"81",
"82",
"83",
"84",
"85",
"86",
"87",
"88",
"89",
"90",
"91",
"92",
"93",
"94",
"95",
"96",
"97",
"98",
"99",
"1000",
"1001"
]
| [
"nonn",
"base",
"easy"
]
| 29 | 1 | 1 | [
"A001633",
"A001637",
"A055642"
]
| null | N. J. A. Sloane | 2022-11-11T08:07:53 | oeisdata/seq/A001/A001637.seq | ce9d42304bd0d02d571de97b48a3f140 |
A001638 | A Fielder sequence: a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4. | [
"4",
"1",
"1",
"4",
"9",
"11",
"16",
"29",
"49",
"76",
"121",
"199",
"324",
"521",
"841",
"1364",
"2209",
"3571",
"5776",
"9349",
"15129",
"24476",
"39601",
"64079",
"103684",
"167761",
"271441",
"439204",
"710649",
"1149851",
"1860496",
"3010349",
"4870849",
"7881196",
"12752041",
"20633239",
"33385284",
"54018521",
"87403801"
]
| [
"nonn",
"easy"
]
| 78 | 0 | 1 | [
"A000032",
"A001609",
"A001634",
"A001636",
"A001638",
"A001645",
"A001648",
"A001649"
]
| [
"M3351",
"N1348"
]
| N. J. A. Sloane | 2025-05-01T01:35:28 | oeisdata/seq/A001/A001638.seq | 4a9cda4db4cf4756ed91293eec944a36 |
A001639 | A Fielder sequence. a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5), n >= 6. | [
"1",
"1",
"4",
"9",
"16",
"22",
"36",
"65",
"112",
"186",
"309",
"522",
"885",
"1492",
"2509",
"4225",
"7124",
"12010",
"20236",
"34094",
"57453",
"96823",
"163163",
"274946",
"463316",
"780755",
"1315687",
"2217112",
"3736129",
"6295887",
"10609441",
"17878369",
"30127497",
"50768954",
"85552651",
"144167958",
"242942778"
]
| [
"nonn"
]
| 45 | 1 | 3 | [
"A000570",
"A001639"
]
| [
"M3353",
"N1349"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001639.seq | 4dd721feed3729d4060b993a4cfe2ed9 |
A001640 | A Fielder sequence. | [
"1",
"1",
"4",
"9",
"16",
"28",
"43",
"73",
"130",
"226",
"386",
"660",
"1132",
"1947",
"3349",
"5753",
"9878",
"16966",
"29147",
"50074",
"86020",
"147764",
"253829",
"436036",
"749041",
"1286728",
"2210377",
"3797047",
"6522681",
"11204863",
"19248056",
"33064889",
"56799857",
"97572504",
"167612993",
"287930658",
"494615964"
]
| [
"nonn"
]
| 39 | 1 | 3 | null | [
"M3358",
"N1352"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001640.seq | f4d12084569fa287884dab9377150147 |
A001641 | A Fielder sequence: a(n) = a(n-1) + a(n-2) + a(n-4). | [
"1",
"3",
"4",
"11",
"16",
"30",
"50",
"91",
"157",
"278",
"485",
"854",
"1496",
"2628",
"4609",
"8091",
"14196",
"24915",
"43720",
"76726",
"134642",
"236283",
"414645",
"727654",
"1276941",
"2240878",
"3932464",
"6900996",
"12110401",
"21252275",
"37295140",
"65448411",
"114853952",
"201554638",
"353703730",
"620706779"
]
| [
"nonn",
"easy"
]
| 66 | 1 | 2 | [
"A001609",
"A001634",
"A001636",
"A001638",
"A001641",
"A001645",
"A001648",
"A001649",
"A060945"
]
| [
"M2364",
"N0935"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001641.seq | c1b72a1fe0f568d444d841a5e2f73225 |
A001642 | A Fielder sequence. | [
"1",
"3",
"4",
"11",
"21",
"36",
"64",
"115",
"211",
"383",
"694",
"1256",
"2276",
"4126",
"7479",
"13555",
"24566",
"44523",
"80694",
"146251",
"265066",
"480406",
"870689",
"1578040",
"2860046",
"5183558",
"9394699",
"17026986",
"30859771",
"55930361",
"101368389",
"183720435",
"332975581",
"603486148",
"1093760479"
]
| [
"nonn"
]
| 42 | 1 | 2 | null | [
"M2367",
"N0937"
]
| N. J. A. Sloane | 2025-02-06T13:16:21 | oeisdata/seq/A001/A001642.seq | cdd0e0c55c3c3d298d76bc233a0e21ad |
A001643 | A Fielder sequence. | [
"1",
"3",
"4",
"11",
"21",
"42",
"71",
"131",
"238",
"443",
"815",
"1502",
"2757",
"5071",
"9324",
"17155",
"31553",
"58038",
"106743",
"196331",
"361106",
"664183",
"1221623",
"2246918",
"4132721",
"7601259",
"13980892",
"25714875",
"47297029",
"86992802",
"160004703",
"294294531",
"541292030",
"995591267",
"1831177831"
]
| [
"nonn"
]
| 45 | 1 | 2 | [
"A001643",
"A001644"
]
| [
"M2368",
"N0938"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001643.seq | b61bb001b27bd69238e1b80ea140a7be |
A001644 | a(n) = a(n-1) + a(n-2) + a(n-3), a(0)=3, a(1)=1, a(2)=3. | [
"3",
"1",
"3",
"7",
"11",
"21",
"39",
"71",
"131",
"241",
"443",
"815",
"1499",
"2757",
"5071",
"9327",
"17155",
"31553",
"58035",
"106743",
"196331",
"361109",
"664183",
"1221623",
"2246915",
"4132721",
"7601259",
"13980895",
"25714875",
"47297029",
"86992799",
"160004703",
"294294531",
"541292033",
"995591267",
"1831177831"
]
| [
"nonn",
"easy"
]
| 272 | 0 | 1 | [
"A000073",
"A001609",
"A001634",
"A001636",
"A001638",
"A001644",
"A001645",
"A001648",
"A001649",
"A058265",
"A073145",
"A073728",
"A106293"
]
| [
"M2625",
"N1040"
]
| N. J. A. Sloane | 2025-05-02T10:22:20 | oeisdata/seq/A001/A001644.seq | 911ef9c4df13a8582a102cc676570c76 |
A001645 | A Fielder sequence. | [
"1",
"3",
"7",
"11",
"26",
"45",
"85",
"163",
"304",
"578",
"1090",
"2057",
"3888",
"7339",
"13862",
"26179",
"49437",
"93366",
"176321",
"332986",
"628852",
"1187596",
"2242800",
"4235569",
"7998951",
"15106172",
"28528288",
"53876211",
"101746240",
"192149690",
"362878313",
"685302531",
"1294206745",
"2444133829"
]
| [
"nonn",
"easy"
]
| 40 | 1 | 2 | [
"A001609",
"A001634",
"A001636",
"A001638",
"A001645",
"A001648",
"A001649"
]
| [
"M2626",
"N1041"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001645.seq | 1d8350a12b98a69cc19f77f48fb01b08 |
A001646 | Number of self-dual codes of length 2n over GF(4). | [
"1",
"1",
"1",
"2",
"3",
"5",
"10",
"21",
"55",
"245",
"3427"
]
| [
"nonn",
"hard",
"more"
]
| 21 | 0 | 4 | null | null | N. J. A. Sloane | 2021-09-14T01:11:56 | oeisdata/seq/A001/A001646.seq | 335d14cc6b0bcd0d54839950719695cf |
A001647 | Number of indecomposable self-dual codes of length 2n over GF(4). | [
"1",
"0",
"1",
"1",
"2",
"4",
"10",
"31"
]
| [
"nonn",
"hard",
"nice",
"more"
]
| 15 | 1 | 5 | null | null | N. J. A. Sloane | 2022-03-12T21:41:15 | oeisdata/seq/A001/A001647.seq | 72b4dae58ac35e3aebb36176d4364cb1 |
A001648 | Tetranacci numbers A073817 without the leading term 4. | [
"1",
"3",
"7",
"15",
"26",
"51",
"99",
"191",
"367",
"708",
"1365",
"2631",
"5071",
"9775",
"18842",
"36319",
"70007",
"134943",
"260111",
"501380",
"966441",
"1862875",
"3590807",
"6921503",
"13341626",
"25716811",
"49570747",
"95550687",
"184179871",
"355018116",
"684319421",
"1319068095",
"2542585503",
"4900991135"
]
| [
"nonn",
"easy"
]
| 72 | 1 | 2 | [
"A000288",
"A001648",
"A073817"
]
| [
"M2648",
"N1055"
]
| N. J. A. Sloane | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001648.seq | 7baee41efa40b238428042aa70778078 |
A001649 | A Fielder sequence. | [
"1",
"3",
"7",
"15",
"26",
"57",
"106",
"207",
"403",
"788",
"1530",
"2985",
"5812",
"11322",
"22052",
"42959",
"83675",
"162993",
"317491",
"618440",
"1204651",
"2346534",
"4570791",
"8903409",
"17342876",
"33782050",
"65803777",
"128178646",
"249678140",
"486346022",
"947349461",
"1845334319",
"3594511719",
"7001720167"
]
| [
"nonn"
]
| 37 | 1 | 2 | null | [
"M2649",
"N1056"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001649.seq | 8d055c145603ccfb941ca3c8d4264312 |
A001650 | k appears k times (k odd). | [
"1",
"3",
"3",
"3",
"5",
"5",
"5",
"5",
"5",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"17",
"17",
"17",
"17",
"17",
"17",
"17",
"17",
"17",
"17",
"17",
"17",
"17"
]
| [
"nonn",
"easy"
]
| 41 | 1 | 2 | [
"A000122",
"A001650",
"A001670",
"A003881",
"A111650",
"A131507",
"A193832"
]
| null | N. J. A. Sloane | 2024-11-24T01:49:37 | oeisdata/seq/A001/A001650.seq | d844f0ad12bd162d9f0203ceb0c8d688 |
A001651 | Numbers not divisible by 3. | [
"1",
"2",
"4",
"5",
"7",
"8",
"10",
"11",
"13",
"14",
"16",
"17",
"19",
"20",
"22",
"23",
"25",
"26",
"28",
"29",
"31",
"32",
"34",
"35",
"37",
"38",
"40",
"41",
"43",
"44",
"46",
"47",
"49",
"50",
"52",
"53",
"55",
"56",
"58",
"59",
"61",
"62",
"64",
"65",
"67",
"68",
"70",
"71",
"73",
"74",
"76",
"77",
"79",
"80",
"82",
"83",
"85",
"86",
"88",
"89",
"91",
"92",
"94",
"95",
"97",
"98",
"100",
"101",
"103",
"104"
]
| [
"nonn",
"easy"
]
| 303 | 1 | 2 | [
"A000027",
"A000217",
"A000292",
"A000726",
"A000982",
"A001082",
"A001477",
"A001651",
"A003105",
"A004526",
"A005408",
"A007494",
"A008585",
"A008619",
"A011655",
"A014437",
"A026386",
"A032766",
"A040001",
"A047239",
"A047257",
"A059564",
"A073010",
"A077043",
"A084858",
"A113801",
"A141425",
"A191967",
"A215879",
"A225227",
"A248897"
]
| [
"M0957",
"N0357"
]
| N. J. A. Sloane | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001651.seq | 6f0e3861f5be6a57a513fe8aa6e83025 |
A001652 | a(n) = 6*a(n-1) - a(n-2) + 2 with a(0) = 0, a(1) = 3. | [
"0",
"3",
"20",
"119",
"696",
"4059",
"23660",
"137903",
"803760",
"4684659",
"27304196",
"159140519",
"927538920",
"5406093003",
"31509019100",
"183648021599",
"1070379110496",
"6238626641379",
"36361380737780",
"211929657785303",
"1235216565974040",
"7199369738058939",
"41961001862379596",
"244566641436218639"
]
| [
"nonn",
"easy",
"nice"
]
| 424 | 0 | 2 | [
"A000129",
"A000217",
"A001108",
"A001109",
"A001333",
"A001541",
"A001542",
"A001652",
"A001653",
"A001921",
"A002024",
"A002315",
"A002378",
"A006451",
"A029549",
"A046090",
"A048739",
"A053141",
"A053142",
"A055997",
"A075841",
"A084159",
"A084703",
"A089950",
"A097571",
"A123737",
"A129556",
"A143608",
"A156035",
"A233450",
"A274307"
]
| [
"M3074",
"N1247"
]
| N. J. A. Sloane | 2025-03-24T12:37:26 | oeisdata/seq/A001/A001652.seq | e006970b326d0ff3aa3d163734525210 |
A001653 | Numbers k such that 2*k^2 - 1 is a square. | [
"1",
"5",
"29",
"169",
"985",
"5741",
"33461",
"195025",
"1136689",
"6625109",
"38613965",
"225058681",
"1311738121",
"7645370045",
"44560482149",
"259717522849",
"1513744654945",
"8822750406821",
"51422757785981",
"299713796309065",
"1746860020068409",
"10181446324101389",
"59341817924539925"
]
| [
"nonn",
"easy",
"nice"
]
| 461 | 1 | 2 | [
"A000217",
"A000290",
"A001109",
"A001519",
"A001652",
"A001653",
"A002315",
"A002559",
"A005054",
"A005319",
"A046090",
"A056220",
"A056869",
"A069894",
"A094954",
"A122074",
"A188647",
"A238379"
]
| [
"M3955",
"N1630"
]
| N. J. A. Sloane | 2025-05-31T05:19:25 | oeisdata/seq/A001/A001653.seq | 7232fe616edd401262a608dc91b08fb5 |
A001654 | Golden rectangle numbers: F(n) * F(n+1), where F(n) = A000045(n) (Fibonacci numbers). | [
"0",
"1",
"2",
"6",
"15",
"40",
"104",
"273",
"714",
"1870",
"4895",
"12816",
"33552",
"87841",
"229970",
"602070",
"1576239",
"4126648",
"10803704",
"28284465",
"74049690",
"193864606",
"507544127",
"1328767776",
"3478759200",
"9107509825",
"23843770274",
"62423800998",
"163427632719",
"427859097160",
"1120149658760"
]
| [
"nonn",
"easy"
]
| 311 | 0 | 3 | [
"A000071",
"A001654",
"A001655",
"A001656",
"A001657",
"A001658",
"A005968",
"A005969",
"A006498",
"A007598",
"A010048",
"A064831",
"A067962",
"A070550",
"A079472",
"A080145",
"A080239",
"A098531",
"A098532",
"A098533",
"A119283",
"A128697",
"A239798",
"A290565"
]
| [
"M1606",
"N0628"
]
| N. J. A. Sloane | 2025-05-31T05:18:36 | oeisdata/seq/A001/A001654.seq | 5e6b95e5b7b49d91bcc9033c23eee576 |
A001655 | Fibonomial coefficients: a(n) = F(n+1) * F(n+2) * F(n+3)/2, where F() = Fibonacci numbers A000045. | [
"1",
"3",
"15",
"60",
"260",
"1092",
"4641",
"19635",
"83215",
"352440",
"1493064",
"6324552",
"26791505",
"113490195",
"480752895",
"2036500788",
"8626757644",
"36543528780",
"154800876945",
"655747029795",
"2777789007071",
"11766903040368",
"49845401197200",
"211148507782800",
"894439432403425"
]
| [
"nonn",
"easy"
]
| 156 | 0 | 2 | [
"A000045",
"A001655",
"A055870",
"A065563",
"A066258",
"A079586",
"A114525",
"A215037",
"A256178",
"A363753"
]
| [
"M2988",
"N1208"
]
| N. J. A. Sloane | 2025-05-07T11:18:06 | oeisdata/seq/A001/A001655.seq | 4dec7f0baee4be94c836c959d3216ab9 |
A001656 | Fibonomial coefficients. | [
"1",
"5",
"40",
"260",
"1820",
"12376",
"85085",
"582505",
"3994320",
"27372840",
"187628376",
"1285992240",
"8814405145",
"60414613805",
"414088493560",
"2838203264876",
"19453338487220",
"133335155341960",
"913892777190965",
"6263914210945105"
]
| [
"nonn",
"easy"
]
| 84 | 0 | 2 | [
"A001622",
"A001654",
"A001655",
"A001656",
"A001657",
"A001658",
"A084175",
"A099930"
]
| [
"M3989",
"N1653"
]
| N. J. A. Sloane | 2025-01-23T12:44:16 | oeisdata/seq/A001/A001656.seq | 746aed1ca1a504c1790e39327e1f8e6c |
A001657 | Fibonomial coefficients: column 5 of A010048. | [
"1",
"8",
"104",
"1092",
"12376",
"136136",
"1514513",
"16776144",
"186135312",
"2063912136",
"22890661872",
"253854868176",
"2815321003313",
"31222272414424",
"346260798314872",
"3840089017377228",
"42587248616222024",
"472299787252290712",
"5237885063192296801",
"58089034826620525728"
]
| [
"nonn",
"easy"
]
| 77 | 0 | 2 | [
"A001654",
"A001657",
"A001658",
"A010048",
"A065563"
]
| [
"M4568",
"N1945"
]
| N. J. A. Sloane | 2025-05-07T11:14:31 | oeisdata/seq/A001/A001657.seq | 4d4679cb89849ef2567da1be076d75ae |
A001658 | Fibonomial coefficients. | [
"1",
"13",
"273",
"4641",
"85085",
"1514513",
"27261234",
"488605194",
"8771626578",
"157373300370",
"2824135408458",
"50675778059634",
"909348684070099",
"16317540120588343",
"292806787575013635",
"5254201798026392211",
"94282845030238533383",
"1691836875411111866723",
"30358781826262552258596"
]
| [
"nonn",
"easy"
]
| 79 | 0 | 2 | [
"A001654",
"A001656",
"A001657",
"A001658"
]
| [
"M4919",
"N2112"
]
| N. J. A. Sloane | 2025-05-07T11:13:20 | oeisdata/seq/A001/A001658.seq | dd3d39a7d519d9f46841798c9c4b410a |
A001659 | Expansion of bracket function. | [
"1",
"1",
"-1",
"2",
"-5",
"13",
"-33",
"80",
"-184",
"402",
"-840",
"1699",
"-3382",
"6750",
"-13716",
"28550",
"-60587",
"129579",
"-275915",
"579828",
"-1197649",
"2431775",
"-4870105",
"9672634",
"-19173013",
"38151533",
"-76521331",
"154941608",
"-316399235",
"649807589",
"-1337598675",
"2751021907",
"-5640238583",
"11513062785",
"-23389948481",
"47310801199",
"-95345789479",
"191616365385"
]
| [
"sign"
]
| 41 | 1 | 4 | [
"A000005",
"A000748",
"A000749",
"A000750",
"A001659",
"A006090",
"A006218",
"A038200"
]
| [
"M1433",
"N0567"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001659.seq | 3b53f109527067ffefcb8e76be61f9ad |
A001660 | Hypotenusal numbers. | [
"1",
"1",
"2",
"6",
"36",
"876",
"408696",
"83762796636",
"3508125906207095591916",
"6153473687096578758445014683368786661634996",
"18932619208894981833333582059033329370801260096062214926751788496235698477988081702676"
]
| [
"nonn",
"easy",
"nice"
]
| 23 | 0 | 3 | [
"A000905",
"A001660"
]
| [
"M1706",
"N0675"
]
| N. J. A. Sloane | 2015-10-12T23:05:16 | oeisdata/seq/A001/A001660.seq | c5dfcf7682661cecbfb93ad77c749397 |
A001661 | Largest number not the sum of distinct positive n-th powers. | [
"128",
"12758",
"5134240",
"67898771",
"11146309947",
"766834015734",
"4968618780985762"
]
| [
"nonn",
"nice",
"more",
"hard"
]
| 103 | 2 | 1 | [
"A001661",
"A030052",
"A121571",
"A173563",
"A279529"
]
| [
"M5393",
"N2342"
]
| N. J. A. Sloane and Robert G. Wilson v | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001661.seq | 45e39d027dfd2f3a121c7be444296bdb |
A001662 | Coefficients of Airey's converging factor. | [
"0",
"1",
"1",
"-1",
"-1",
"13",
"-47",
"-73",
"2447",
"-16811",
"-15551",
"1726511",
"-18994849",
"10979677",
"2983409137",
"-48421103257",
"135002366063",
"10125320047141",
"-232033147779359",
"1305952009204319",
"58740282660173759",
"-1862057132555380307",
"16905219421196907793",
"527257187244811805207"
]
| [
"sign",
"easy",
"nice"
]
| 239 | 0 | 6 | [
"A001662",
"A032188",
"A051711",
"A274447",
"A274448",
"A340556"
]
| [
"M4896",
"N2098"
]
| N. J. A. Sloane | 2025-07-02T16:01:54 | oeisdata/seq/A001/A001662.seq | 0f1365449a451ef3ce4d2537cfdab8bb |
A001663 | Linear coefficient of the n-th converging polynomial of Weber functions (Erroneous version). | [
"1",
"-3",
"7",
"-5",
"-93",
"637",
"-1425",
"-22341"
]
| [
"sign"
]
| 38 | 1 | 2 | [
"A001662",
"A001663",
"A001664",
"A380170"
]
| [
"M2610",
"N1032"
]
| N. J. A. Sloane | 2025-01-14T09:58:24 | oeisdata/seq/A001/A001663.seq | c1dcfb8e288efed9d272d3b88a668182 |
A001664 | Quadratic coefficient of the n-th converging polynomial of Weber functions. | [
"1",
"-6",
"25",
"-60",
"-203",
"3710",
"-21347",
"-50400",
"2465969",
"-24201342",
"-14909791",
"4154706556",
"-61829802067",
"107889525510",
"13926895008805",
"-296622934827816",
"1387504872714793",
"80367331405832714",
"-2381736125794455767",
"19480923855903871284",
"721535152036700012069",
"-29550684521199839783538"
]
| [
"sign"
]
| 28 | 2 | 2 | [
"A001662",
"A001663",
"A001664"
]
| [
"M4165",
"N1732"
]
| N. J. A. Sloane | 2025-01-13T15:19:08 | oeisdata/seq/A001/A001664.seq | e0dfbfc366652d1624bc4c3188d7804e |
A001665 | Number of self-avoiding n-step walks on Kagome lattice. | [
"1",
"4",
"12",
"32",
"88",
"240",
"652",
"1744",
"4616",
"12208",
"32328",
"85408",
"224640",
"589024",
"1542944",
"4039256",
"10560552",
"27567488",
"71878068",
"187262944",
"487526944",
"1268269160",
"3296832292",
"8564411120",
"22235825104",
"57701041072",
"149657337872",
"387978891176",
"1005378745536",
"2604222063144",
"6743181213712",
"17454178002264"
]
| [
"nonn",
"walk",
"nice"
]
| 20 | 0 | 2 | null | [
"M3445",
"N1399"
]
| N. J. A. Sloane | 2024-10-18T11:43:27 | oeisdata/seq/A001/A001665.seq | 92ceca1f0977079e3b4a17c29303fefe |
A001666 | Number of n-step self-avoiding walks on b.c.c. lattice (version 2). | [
"1",
"8",
"56",
"392",
"2648",
"17960",
"120056",
"804824",
"5351720",
"35652680",
"236291096",
"1568049560",
"10368669992",
"68626647608",
"453032542040",
"2992783648424",
"19731335857592",
"130161040083608",
"857282278813256",
"5648892048530888",
"37175039569217672",
"244738250638121768"
]
| [
"nonn",
"walk",
"nice"
]
| 32 | 0 | 2 | [
"A001336",
"A001412",
"A001666",
"A002903"
]
| [
"M4545",
"N1929"
]
| N. J. A. Sloane | 2022-10-16T13:26:01 | oeisdata/seq/A001/A001666.seq | ba94a91225c75a8e066cae411f875507 |
A001667 | 2n-step polygons on b.c.c. lattice. | [
"96",
"1776",
"43776",
"1237920",
"37903776",
"1223681760",
"41040797376",
"1416762272736",
"50027402384640",
"1799035070369856"
]
| [
"nonn",
"nice",
"walk",
"more"
]
| 25 | 2 | 1 | [
"A001337",
"A001413",
"A001666",
"A001667",
"A038515"
]
| [
"M5364",
"N2330"
]
| N. J. A. Sloane | 2022-06-03T01:43:22 | oeisdata/seq/A001/A001667.seq | 7c2b767ea24bb32b7e458b4041bc9f24 |
A001668 | Number of self-avoiding n-step walks on honeycomb lattice. | [
"1",
"3",
"6",
"12",
"24",
"48",
"90",
"174",
"336",
"648",
"1218",
"2328",
"4416",
"8388",
"15780",
"29892",
"56268",
"106200",
"199350",
"375504",
"704304",
"1323996",
"2479692",
"4654464",
"8710212",
"16328220",
"30526374",
"57161568",
"106794084",
"199788408",
"372996450",
"697217994",
"1300954248"
]
| [
"nonn",
"walk",
"nice"
]
| 60 | 0 | 2 | [
"A001668",
"A006851"
]
| [
"M2559",
"N1013"
]
| N. J. A. Sloane | 2024-08-08T11:06:25 | oeisdata/seq/A001/A001668.seq | 7cf9266d1e9daee0f0b3fdd74ef4dc48 |
A001669 | Number of 7-level labeled rooted trees with n leaves. | [
"1",
"1",
"7",
"70",
"910",
"14532",
"274778",
"5995892",
"148154860",
"4085619622",
"124304629050",
"4133867297490",
"149114120602860",
"5796433459664946",
"241482353893283349",
"10730629952953517859",
"506500241174366575122",
"25302666611855946733140"
]
| [
"nonn",
"easy"
]
| 46 | 0 | 3 | [
"A000110",
"A000258",
"A000307",
"A000357",
"A000405",
"A001669",
"A144150"
]
| [
"M4443",
"N1879"
]
| N. J. A. Sloane | 2022-02-01T01:21:37 | oeisdata/seq/A001/A001669.seq | 1fd331f9d2c2a6c36be8ee6010ae42be |
A001670 | k appears k times (k even). | [
"2",
"2",
"4",
"4",
"4",
"4",
"6",
"6",
"6",
"6",
"6",
"6",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"10",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"14",
"14",
"14",
"14",
"14",
"14",
"14",
"14",
"14",
"14",
"14",
"14",
"14",
"14",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16"
]
| [
"nonn",
"easy"
]
| 48 | 1 | 1 | [
"A000194",
"A001650",
"A001670",
"A130829"
]
| null | N. J. A. Sloane | 2025-05-08T07:22:46 | oeisdata/seq/A001/A001670.seq | de936edfc5020e8842788b26063e3e1a |
A001671 | Powers of e rounded up. | [
"1",
"3",
"8",
"21",
"55",
"149",
"404",
"1097",
"2981",
"8104",
"22027",
"59875",
"162755",
"442414",
"1202605",
"3269018",
"8886111",
"24154953",
"65659970",
"178482301",
"485165196",
"1318815735",
"3584912847",
"9744803447",
"26489122130",
"72004899338",
"195729609429",
"532048240602",
"1446257064292",
"3931334297145",
"10686474581525"
]
| [
"nonn"
]
| 17 | 0 | 2 | [
"A000149",
"A000227",
"A001671"
]
| null | N. J. A. Sloane | 2018-05-28T15:35:59 | oeisdata/seq/A001/A001671.seq | 7f046dce020280f02ab7e3bf2b825ea0 |
A001672 | a(n) = floor(Pi^n). | [
"1",
"3",
"9",
"31",
"97",
"306",
"961",
"3020",
"9488",
"29809",
"93648",
"294204",
"924269",
"2903677",
"9122171",
"28658145",
"90032220",
"282844563",
"888582403",
"2791563949",
"8769956796",
"27551631842",
"86556004191",
"271923706893",
"854273519913",
"2683779414317",
"8431341691876",
"26487841119103"
]
| [
"nonn"
]
| 23 | 0 | 2 | [
"A001672",
"A001673",
"A002160"
]
| null | N. J. A. Sloane | 2018-05-28T14:22:40 | oeisdata/seq/A001/A001672.seq | a791278775291ca2d81c59ab6b615ee2 |
A001673 | a(n) = ceiling(Pi^n). | [
"1",
"4",
"10",
"32",
"98",
"307",
"962",
"3021",
"9489",
"29810",
"93649",
"294205",
"924270",
"2903678",
"9122172",
"28658146",
"90032221",
"282844564",
"888582404",
"2791563950",
"8769956797",
"27551631843",
"86556004192",
"271923706894",
"854273519914",
"2683779414318",
"8431341691877",
"26487841119104"
]
| [
"nonn"
]
| 12 | 0 | 2 | null | null | N. J. A. Sloane | 2016-12-19T01:20:59 | oeisdata/seq/A001/A001673.seq | a01119909d89789ffc92ac7d66f36c0c |
A001674 | a(n) = floor(sqrt( 2*Pi )^n). | [
"1",
"2",
"6",
"15",
"39",
"98",
"248",
"621",
"1558",
"3906",
"9792",
"24546",
"61528",
"154230",
"386597",
"969056",
"2429063",
"6088760",
"15262258",
"38256809",
"95895600",
"240374623",
"602529828",
"1510318305",
"3785806567",
"9489609784",
"23786924200",
"59624976768",
"149457652641",
"374634777972"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A000149",
"A001672",
"A001674",
"A014217",
"A017910",
"A032739",
"A062541",
"A121831"
]
| null | N. J. A. Sloane | 2022-02-01T01:21:53 | oeisdata/seq/A001/A001674.seq | cd90cf1078204cc766e85c95e734e3a9 |
A001675 | a(n) = round(sqrt( 2*Pi )^n). | [
"1",
"3",
"6",
"16",
"39",
"99",
"248",
"622",
"1559",
"3907",
"9793",
"24546",
"61529",
"154230",
"386598",
"969056",
"2429064",
"6088760",
"15262259",
"38256810",
"95895601",
"240374624",
"602529829",
"1510318305",
"3785806568",
"9489609784",
"23786924201",
"59624976768",
"149457652642",
"374634777972"
]
| [
"nonn"
]
| 16 | 0 | 2 | [
"A000227",
"A001674",
"A001675",
"A001698",
"A002160",
"A017911"
]
| null | N. J. A. Sloane | 2022-02-01T01:22:08 | oeisdata/seq/A001/A001675.seq | 42aeeaee42da35fb085c6ef29e596afc |
A001676 | Number of h-cobordism classes of smooth homotopy n-spheres. | [
"1",
"1",
"1",
"1",
"1",
"1",
"28",
"2",
"8",
"6",
"992",
"1",
"3",
"2",
"16256",
"2",
"16",
"16",
"523264",
"24",
"8",
"4",
"69524373504",
"2",
"4",
"12",
"67100672",
"2",
"3",
"3",
"7767211311104",
"8",
"32",
"32",
"3014494287036416",
"6",
"24",
"120",
"2303837503821447168",
"192",
"32",
"96",
"341653284209033216",
"8",
"11520",
"48",
"798366828940770681028608",
"32",
"12",
"24",
"11852230872517975212032",
"24",
"32",
"8",
"91678339751618435453288448",
"1",
"8",
"4",
"1986677733776616536315084668928",
"4",
"1",
"24",
"284423744326342962334231917756416"
]
| [
"nonn",
"hard",
"nice"
]
| 102 | 1 | 7 | [
"A001676",
"A048648",
"A053381",
"A057617",
"A187595",
"A187717",
"A189995",
"A191783",
"A228689",
"A228690",
"A228691",
"A228692"
]
| [
"M5197",
"N2261"
]
| N. J. A. Sloane | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001676.seq | b9e9191e9a574631a3e1505ff18f5b44 |
A001677 | Number of series-parallel networks with n edges. | [
"1",
"2",
"3",
"6",
"12",
"26",
"59",
"146",
"368",
"976",
"2667",
"7482",
"21440",
"62622",
"185637",
"557680",
"1694256",
"5198142",
"16086486",
"50165218",
"157510504",
"497607008",
"1580800091",
"5047337994",
"16190223624",
"52153429218",
"168657986843",
"547389492416"
]
| [
"nonn",
"nice",
"easy",
"changed"
]
| 32 | 2 | 2 | [
"A001677",
"A058642",
"A058668"
]
| [
"M0797",
"N0302"
]
| N. J. A. Sloane | 2025-07-08T16:26:52 | oeisdata/seq/A001/A001677.seq | 20ae04eae60aa5a8f9f17d23e082a26e |
A001678 | Number of series-reduced planted trees with n nodes. | [
"0",
"0",
"1",
"0",
"1",
"1",
"2",
"3",
"6",
"10",
"19",
"35",
"67",
"127",
"248",
"482",
"952",
"1885",
"3765",
"7546",
"15221",
"30802",
"62620",
"127702",
"261335",
"536278",
"1103600",
"2276499",
"4706985",
"9752585",
"20247033",
"42110393",
"87733197",
"183074638",
"382599946",
"800701320",
"1677922740",
"3520581954"
]
| [
"nonn",
"easy",
"nice"
]
| 102 | 0 | 7 | [
"A000014",
"A000081",
"A000669",
"A001678",
"A001679",
"A004111",
"A005202",
"A007827",
"A060356",
"A106179",
"A108919",
"A198518",
"A246403",
"A254382",
"A291636",
"A330951",
"A331488",
"A331578"
]
| [
"M0768",
"N0293"
]
| N. J. A. Sloane | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001678.seq | 310ece5eee20818c44f9dfcf46d3ff6d |
A001679 | Number of series-reduced rooted trees with n nodes. | [
"1",
"1",
"1",
"0",
"2",
"2",
"4",
"6",
"12",
"20",
"39",
"71",
"137",
"261",
"511",
"995",
"1974",
"3915",
"7841",
"15749",
"31835",
"64540",
"131453",
"268498",
"550324",
"1130899",
"2330381",
"4813031",
"9963288",
"20665781",
"42947715",
"89410092",
"186447559",
"389397778",
"814447067",
"1705775653",
"3577169927"
]
| [
"nonn"
]
| 62 | 0 | 5 | [
"A000014",
"A000055",
"A000081",
"A000669",
"A001678",
"A001679",
"A004111",
"A005512",
"A059123",
"A060313",
"A060356",
"A198518",
"A246403",
"A254382",
"A291636",
"A330951",
"A331488",
"A331489",
"A331578"
]
| [
"M0327",
"N0123"
]
| N. J. A. Sloane | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001679.seq | e43e3b6d6987999701989d2615260691 |
A001680 | The partition function G(n,3). | [
"1",
"1",
"2",
"5",
"14",
"46",
"166",
"652",
"2780",
"12644",
"61136",
"312676",
"1680592",
"9467680",
"55704104",
"341185496",
"2170853456",
"14314313872",
"97620050080",
"687418278544",
"4989946902176",
"37286121988256",
"286432845428192",
"2259405263572480",
"18280749571449664",
"151561941235370176"
]
| [
"nonn",
"changed"
]
| 86 | 0 | 3 | [
"A001680",
"A001681",
"A189886",
"A229223"
]
| [
"M1465",
"N0579"
]
| N. J. A. Sloane | 2025-07-08T00:15:01 | oeisdata/seq/A001/A001680.seq | 66e0c00a95b311eaad5618c453913d20 |
A001681 | The partition function G(n,4). | [
"1",
"1",
"2",
"5",
"15",
"51",
"196",
"827",
"3795",
"18755",
"99146",
"556711",
"3305017",
"20655285",
"135399720",
"927973061",
"6631556521",
"49294051497",
"380306658250",
"3039453750685",
"25120541332271",
"214363100120051",
"1885987611214092",
"17085579637664715",
"159185637725413675"
]
| [
"nonn",
"easy"
]
| 74 | 0 | 3 | [
"A001680",
"A001681",
"A229223",
"A276924"
]
| [
"M1481",
"N0584"
]
| N. J. A. Sloane | 2018-02-26T09:03:51 | oeisdata/seq/A001/A001681.seq | 16709e1a72bdd9e8c05e757f48aa485a |
A001682 | Numbers k such that 3^k, 3^(k+1) and 3^(k+2) have the same number of digits. | [
"0",
"21",
"42",
"65",
"86",
"109",
"130",
"151",
"174",
"195",
"218",
"239",
"262",
"283",
"304",
"327",
"348",
"371",
"392",
"415",
"436",
"457",
"480",
"501",
"524",
"545",
"568",
"589",
"610",
"633",
"654",
"677",
"698",
"721",
"742",
"763",
"786",
"807",
"830",
"851",
"874",
"895",
"916",
"939",
"960",
"983",
"1004",
"1027",
"1048"
]
| [
"nonn",
"base",
"easy",
"nice"
]
| 36 | 1 | 2 | [
"A000244",
"A001682",
"A055642",
"A151910"
]
| [
"M5109",
"N2213"
]
| N. J. A. Sloane | 2021-02-11T23:00:33 | oeisdata/seq/A001/A001682.seq | f0b9dbf6e0b185f9d621885c57eed3b8 |
A001683 | Number of one-sided triangulations of the disk; or flexagons of order n; or unlabeled plane trivalent trees (n-2 internal vertices, all of degree 3 and hence n leaves). | [
"1",
"1",
"1",
"1",
"4",
"6",
"19",
"49",
"150",
"442",
"1424",
"4522",
"14924",
"49536",
"167367",
"570285",
"1965058",
"6823410",
"23884366",
"84155478",
"298377508",
"1063750740",
"3811803164",
"13722384546",
"49611801980",
"180072089896",
"655977266884",
"2397708652276",
"8791599732140",
"32330394085528"
]
| [
"nonn",
"nice",
"easy"
]
| 115 | 2 | 5 | [
"A000207",
"A001683",
"A005034",
"A007173",
"A007282",
"A057162",
"A208355",
"A262586",
"A295224",
"A369314"
]
| [
"M3288",
"N1325"
]
| N. J. A. Sloane | 2024-04-10T04:09:41 | oeisdata/seq/A001/A001683.seq | 2770ed34060c05caf951b822763c3926 |
A001684 | From a continued fraction. | [
"1",
"1",
"1",
"1",
"2",
"6",
"30",
"390",
"32370",
"81022110",
"79098077953830",
"2499603048957386233742790",
"6399996109983215106481566902449146981585570",
"1296147136591533261616288032775924136752630487513536584267056282299509616710"
]
| [
"nonn"
]
| 22 | 0 | 5 | null | [
"M1693",
"N0669"
]
| N. J. A. Sloane | 2017-06-20T12:24:02 | oeisdata/seq/A001/A001684.seq | 9ef4799575408596cb652ee91b602408 |
A001685 | a(0) = 1, a(1) = 2, a(2) = 3; for n >= 3, a(n) = a(n-2) + a(n-1)*Product_{i=1..n-3} a(i). | [
"1",
"2",
"3",
"5",
"13",
"83",
"2503",
"976253",
"31601312113",
"2560404986164794683",
"202523113189037952478722304798003",
"506227391211661106785411233681995783881012463859772443053"
]
| [
"nonn"
]
| 39 | 0 | 2 | [
"A001685",
"A003686",
"A064526",
"A109134"
]
| [
"M0740",
"N0278"
]
| N. J. A. Sloane | 2017-06-20T12:27:00 | oeisdata/seq/A001/A001685.seq | 9f805df07a73d9418e208a1e09841ac4 |
A001686 | From a continued fraction. | [
"1",
"1",
"2",
"3",
"8",
"51",
"1538",
"599871",
"19417825808",
"1573273218577214751",
"124442887685693556895657990772138",
"311057821480221188367831306672353513246409033360367599771"
]
| [
"nonn"
]
| 21 | 0 | 3 | [
"A001684",
"A001685",
"A001686"
]
| [
"M0893",
"N0338"
]
| N. J. A. Sloane | 2022-02-01T01:22:27 | oeisdata/seq/A001/A001686.seq | 486180825c03cf013b268213e62f03f2 |
A001687 | a(n) = a(n-2) + a(n-5). | [
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"2",
"1",
"3",
"2",
"4",
"4",
"5",
"7",
"7",
"11",
"11",
"16",
"18",
"23",
"29",
"34",
"45",
"52",
"68",
"81",
"102",
"126",
"154",
"194",
"235",
"296",
"361",
"450",
"555",
"685",
"851",
"1046",
"1301",
"1601",
"1986",
"2452",
"3032",
"3753",
"4633",
"5739",
"7085",
"8771",
"10838",
"13404",
"16577",
"20489",
"25348",
"31327"
]
| [
"nonn"
]
| 63 | 0 | 9 | [
"A001687",
"A005686"
]
| [
"M0147",
"N0059"
]
| N. J. A. Sloane, following a suggestion from Robert G. Wilson v | 2022-04-13T13:25:16 | oeisdata/seq/A001/A001687.seq | 22e7e71706eb847e8bc63a10365cac43 |
A001688 | 4th forward differences of factorial numbers A000142. | [
"9",
"53",
"362",
"2790",
"24024",
"229080",
"2399760",
"27422640",
"339696000",
"4536362880",
"64988179200",
"994447238400",
"16190733081600",
"279499828608000",
"5100017213491200",
"98087346669312000",
"1983334021853184000",
"42063950934061056000",
"933754193111900160000"
]
| [
"nonn",
"easy"
]
| 48 | 0 | 1 | [
"A000142",
"A001563",
"A001564",
"A001565",
"A001688",
"A001689",
"A095177"
]
| [
"M4636",
"N1980"
]
| N. J. A. Sloane | 2021-07-27T21:20:05 | oeisdata/seq/A001/A001688.seq | e4ba7752d6c8fbeddf991f034de4686c |
A001689 | 5th forward differences of factorial numbers A000142. | [
"44",
"309",
"2428",
"21234",
"205056",
"2170680",
"25022880",
"312273360",
"4196666880",
"60451816320",
"929459059200",
"15196285843200",
"263309095526400",
"4820517384883200",
"92987329455820800",
"1885246675183872000",
"40080616912207872000",
"891690242177839104000"
]
| [
"nonn",
"easy"
]
| 43 | 0 | 1 | [
"A000142",
"A001563",
"A001564",
"A001565",
"A001688",
"A001689",
"A096307"
]
| [
"M4531",
"N1920"
]
| N. J. A. Sloane | 2021-07-27T04:03:14 | oeisdata/seq/A001/A001689.seq | a29561045450522a808b8b2515d47b5f |
A001690 | Non-Fibonacci numbers. | [
"4",
"6",
"7",
"9",
"10",
"11",
"12",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"33",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"76",
"77",
"78"
]
| [
"nonn",
"easy",
"nice"
]
| 91 | 1 | 1 | [
"A000045",
"A001690",
"A010056"
]
| [
"M3268",
"N1319"
]
| N. J. A. Sloane | 2025-01-05T19:51:32 | oeisdata/seq/A001/A001690.seq | 7c95da2f0195df4fb21f8e93a070c237 |
A001691 | Number of two-element generating sets in the symmetric group S_n. | [
"0",
"1",
"9",
"108",
"3420",
"114480",
"7786800",
"497266560",
"42616445760",
"4320959126400",
"534444478444800",
"77699101730342400",
"13282131639801024000"
]
| [
"nonn",
"more"
]
| 35 | 1 | 3 | [
"A001691",
"A071605",
"A086373"
]
| [
"M4660",
"N1995"
]
| N. J. A. Sloane | 2022-02-01T07:12:34 | oeisdata/seq/A001/A001691.seq | 7ba0999a1740ff1b6327d6169249e59d |
A001692 | Number of irreducible polynomials of degree n over GF(5); dimensions of free Lie algebras. | [
"1",
"5",
"10",
"40",
"150",
"624",
"2580",
"11160",
"48750",
"217000",
"976248",
"4438920",
"20343700",
"93900240",
"435959820",
"2034504992",
"9536718750",
"44878791360",
"211927516500",
"1003867701480",
"4768371093720",
"22706531339280"
]
| [
"nonn",
"nice",
"easy"
]
| 77 | 0 | 2 | [
"A000351",
"A001037",
"A001692",
"A002105",
"A008683",
"A027750",
"A054720",
"A074650"
]
| [
"M3804",
"N1554"
]
| N. J. A. Sloane | 2021-11-17T07:18:03 | oeisdata/seq/A001/A001692.seq | c481c7b280a851621178e797e21b626c |
A001693 | Number of degree-n irreducible polynomials over GF(7); dimensions of free Lie algebras. | [
"1",
"7",
"21",
"112",
"588",
"3360",
"19544",
"117648",
"720300",
"4483696",
"28245840",
"179756976",
"1153430600",
"7453000800",
"48444446376",
"316504099520",
"2077057800300",
"13684147881600",
"90467419857752",
"599941851861744"
]
| [
"nonn",
"easy",
"nice"
]
| 52 | 0 | 2 | [
"A000031",
"A001037",
"A001693",
"A027376",
"A032164",
"A074650"
]
| [
"M4373",
"N1838"
]
| N. J. A. Sloane | 2017-11-22T16:41:10 | oeisdata/seq/A001/A001693.seq | 3e6b9a30dd40d0bf8459b02812565536 |
A001694 | Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers). | [
"1",
"4",
"8",
"9",
"16",
"25",
"27",
"32",
"36",
"49",
"64",
"72",
"81",
"100",
"108",
"121",
"125",
"128",
"144",
"169",
"196",
"200",
"216",
"225",
"243",
"256",
"288",
"289",
"324",
"343",
"361",
"392",
"400",
"432",
"441",
"484",
"500",
"512",
"529",
"576",
"625",
"648",
"675",
"676",
"729",
"784",
"800",
"841",
"864",
"900",
"961",
"968",
"972",
"1000"
]
| [
"nonn",
"nice",
"easy"
]
| 212 | 1 | 2 | [
"A001248",
"A001694",
"A003321",
"A005188",
"A005934",
"A007532",
"A013929",
"A014576",
"A023052",
"A046074",
"A052485",
"A062503",
"A076446",
"A076871",
"A112526",
"A168363",
"A224866",
"A258599",
"A261883",
"A300717",
"A320966",
"A376361",
"A376362"
]
| [
"M3325",
"N1335"
]
| N. J. A. Sloane | 2025-03-28T03:27:13 | oeisdata/seq/A001/A001694.seq | ad901e62c74bd7ef1e023e5436e646e2 |
A001695 | a(n) = H_n(2,n) where H_n is the n-th hyperoperator. | [
"1",
"3",
"4",
"8",
"65536"
]
| [
"nonn",
"nice"
]
| 62 | 0 | 2 | [
"A001695",
"A014221",
"A046859",
"A054871"
]
| [
"M2352",
"N0929"
]
| N. J. A. Sloane, following a suggestion from Robert G. Wilson v, Aug 31 1994 | 2025-02-16T08:32:24 | oeisdata/seq/A001/A001695.seq | 7a88ce831689d24dd4dde8238d6dee93 |
A001696 | a(n) = a(n-1)*(1 + a(n-1) - a(n-2)), a(0) = 0, a(1) = 1. | [
"0",
"1",
"2",
"4",
"12",
"108",
"10476",
"108625644",
"11798392680793836",
"139202068568601568785946949658348",
"19377215893777651167043206536157529523359277782016064519251404524"
]
| [
"nonn",
"easy"
]
| 48 | 0 | 3 | [
"A001696",
"A001697",
"A039941"
]
| [
"M1268",
"N0487"
]
| N. J. A. Sloane | 2025-01-09T08:21:55 | oeisdata/seq/A001/A001696.seq | 73b00a344f265e72321ce46933cbdade |
A001697 | a(n+1) = a(n)(a(0) + ... + a(n)). | [
"1",
"1",
"2",
"8",
"96",
"10368",
"108615168",
"11798392572168192",
"139202068568601556987554268864512",
"19377215893777651167043206536157390321290709180447278572301746176"
]
| [
"nonn",
"easy",
"nice"
]
| 63 | 0 | 3 | [
"A001696",
"A001697",
"A001699",
"A002658",
"A039941",
"A064847"
]
| [
"M1902",
"N0751"
]
| N. J. A. Sloane | 2025-01-09T08:22:47 | oeisdata/seq/A001/A001697.seq | a74e44d6f887c79f706f6f70c1bc4c08 |
A001698 | a(n) = ceiling(sqrt( 2*Pi )^n). | [
"1",
"3",
"7",
"16",
"40",
"99",
"249",
"622",
"1559",
"3907",
"9793",
"24547",
"61529",
"154231",
"386598",
"969057",
"2429064",
"6088761",
"15262259",
"38256810",
"95895601",
"240374624",
"602529829",
"1510318306",
"3785806568",
"9489609785",
"23786924201",
"59624976769",
"149457652642",
"374634777973"
]
| [
"nonn"
]
| 16 | 0 | 2 | null | null | N. J. A. Sloane | 2016-12-19T01:21:32 | oeisdata/seq/A001/A001698.seq | 870999c726da199d020efd1f7327379a |
A001699 | Number of binary trees of height n; or products (ways to insert parentheses) of height n when multiplication is non-commutative and non-associative. | [
"1",
"1",
"3",
"21",
"651",
"457653",
"210065930571",
"44127887745696109598901",
"1947270476915296449559659317606103024276803403",
"3791862310265926082868235028027893277370233150300118107846437701158064808916492244872560821"
]
| [
"nonn",
"easy",
"core",
"nice"
]
| 114 | 0 | 3 | [
"A001699",
"A002449",
"A002658",
"A003095",
"A004019",
"A056207",
"A065329",
"A076949",
"A077496",
"A213437",
"A335919",
"A335920"
]
| [
"M3087",
"N1251"
]
| N. J. A. Sloane and Jeffrey Shallit | 2025-06-06T08:34:45 | oeisdata/seq/A001/A001699.seq | 8b33024a9c87b451b9df1a6100279a91 |
A001700 | a(n) = binomial(2*n+1, n+1): number of ways to put n+1 indistinguishable balls into n+1 distinguishable boxes = number of (n+1)-st degree monomials in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1. | [
"1",
"3",
"10",
"35",
"126",
"462",
"1716",
"6435",
"24310",
"92378",
"352716",
"1352078",
"5200300",
"20058300",
"77558760",
"300540195",
"1166803110",
"4537567650",
"17672631900",
"68923264410",
"269128937220",
"1052049481860",
"4116715363800",
"16123801841550",
"63205303218876",
"247959266474052"
]
| [
"easy",
"nonn",
"nice",
"core"
]
| 688 | 0 | 2 | [
"A000108",
"A000110",
"A000984",
"A001263",
"A001405",
"A001448",
"A001700",
"A001792",
"A001813",
"A002054",
"A002458",
"A005043",
"A005773",
"A007318",
"A028364",
"A030662",
"A035324",
"A039598",
"A046097",
"A049027",
"A050166",
"A060150",
"A060897",
"A060900",
"A073165",
"A076025",
"A076026",
"A088218",
"A091867",
"A100257",
"A102539",
"A103371",
"A110556",
"A132813",
"A134285",
"A138364",
"A166454"
]
| [
"M2848",
"N1144"
]
| N. J. A. Sloane | 2025-05-21T04:46:17 | oeisdata/seq/A001/A001700.seq | 92a4d6ff6cf93db16d8c8f7fb0c03cd5 |
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