sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A001901
|
Successive numerators of Wallis's approximation to Pi/2 (reduced).
|
[
"1",
"2",
"4",
"16",
"64",
"128",
"256",
"2048",
"16384",
"32768",
"65536",
"262144",
"1048576",
"2097152",
"4194304",
"67108864",
"1073741824",
"2147483648",
"4294967296",
"17179869184",
"68719476736",
"137438953472",
"274877906944",
"2199023255552"
] |
[
"nonn",
"frac",
"easy"
] | 54 | 0 | 2 |
[
"A000079",
"A001901",
"A001902"
] | null |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001901.seq
|
5b7e0cc59d6f17c565b9f88e01799647
|
A001902
|
Successive denominators of Wallis's approximation to Pi/2 (reduced).
|
[
"1",
"1",
"3",
"9",
"45",
"75",
"175",
"1225",
"11025",
"19845",
"43659",
"160083",
"693693",
"1288287",
"2760615",
"41409225",
"703956825",
"1329696225",
"2807136475",
"10667118605",
"44801898141",
"85530896451",
"178837328943",
"1371086188563",
"11425718238025"
] |
[
"nonn",
"frac",
"easy"
] | 45 | 0 | 3 |
[
"A000246",
"A001900",
"A001901",
"A001902"
] | null |
N. J. A. Sloane
| 2024-10-19T09:33:59 |
oeisdata/seq/A001/A001902.seq
|
10623940ef8987ff5564ef8245e7a835
|
A001903
|
Final digit of 7^n.
|
[
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1",
"7",
"9",
"3",
"1"
] |
[
"nonn",
"easy"
] | 69 | 0 | 2 |
[
"A000420",
"A001148",
"A001903",
"A010879",
"A131707",
"A159966"
] | null |
N. J. A. Sloane
| 2025-05-21T16:37:37 |
oeisdata/seq/A001/A001903.seq
|
454db8b2d64e078318b696a6ddcc10ca
|
A001904
|
From higher order Bernoulli numbers: absolute value of numerator of D Number D2n(2n).
|
[
"1",
"2",
"88",
"3056",
"319616",
"18940160",
"94645408768",
"526713485312",
"2012969145761792",
"1516106277997969408",
"950096677725742563328",
"125099579935028774699008",
"1308695886352702185064628224",
"7547869395875499805522264064"
] |
[
"nonn",
"frac"
] | 40 | 0 | 2 |
[
"A001904",
"A001905",
"A261272",
"A261274"
] |
[
"M2178",
"N0871"
] |
N. J. A. Sloane
| 2019-07-02T14:13:15 |
oeisdata/seq/A001/A001904.seq
|
1d50631a0666abd3d4af7849ba56ef91
|
A001905
|
From higher-order Bernoulli numbers: absolute value of numerator of D-number D2n(2n-1).
|
[
"1",
"17",
"1835",
"195013",
"3887409",
"58621671097",
"327585142651",
"83717985168643",
"189605076148138997",
"595202561342135705333",
"26162958970171926774263",
"822117399240965474306397043",
"4746533358587697361080419575"
] |
[
"nonn",
"frac"
] | 39 | 1 | 2 |
[
"A001904",
"A001905",
"A261272",
"A261274"
] |
[
"M5051",
"N2184"
] |
N. J. A. Sloane
| 2019-07-02T14:14:02 |
oeisdata/seq/A001/A001905.seq
|
757eb1fadaa9137b969034340a9850fb
|
A001906
|
F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2).
|
[
"0",
"1",
"3",
"8",
"21",
"55",
"144",
"377",
"987",
"2584",
"6765",
"17711",
"46368",
"121393",
"317811",
"832040",
"2178309",
"5702887",
"14930352",
"39088169",
"102334155",
"267914296",
"701408733",
"1836311903",
"4807526976",
"12586269025",
"32951280099",
"86267571272",
"225851433717",
"591286729879",
"1548008755920"
] |
[
"nonn",
"easy",
"nice",
"core"
] | 748 | 0 | 3 |
[
"A000032",
"A000041",
"A000045",
"A001519",
"A001622",
"A001906",
"A033888",
"A033890",
"A048996",
"A052529",
"A055991",
"A058038",
"A078812",
"A130259",
"A130260",
"A153386",
"A249450",
"A305309",
"A344212"
] |
[
"M2741",
"N1101"
] |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001906.seq
|
1f57eede73ead85878938a1ac791a911
|
A001907
|
Expansion of e.g.f. exp(-x)/(1-4*x).
|
[
"1",
"3",
"25",
"299",
"4785",
"95699",
"2296777",
"64309755",
"2057912161",
"74084837795",
"2963393511801",
"130389314519243",
"6258687096923665",
"325451729040030579",
"18225296826241712425",
"1093517809574502745499",
"69985139812768175711937",
"4758989507268235948411715"
] |
[
"easy",
"nonn"
] | 51 | 0 | 2 |
[
"A000166",
"A000180",
"A000354",
"A001907",
"A001908",
"A320032"
] |
[
"M3112",
"N1261"
] |
N. J. A. Sloane
| 2022-09-08T08:44:29 |
oeisdata/seq/A001/A001907.seq
|
3654463f8d025d25c921a47929bb70c4
|
A001908
|
E.g.f. exp(-x)/(1-5*x).
|
[
"1",
"4",
"41",
"614",
"12281",
"307024",
"9210721",
"322375234",
"12895009361",
"580275421244",
"29013771062201",
"1595757408421054",
"95745444505263241",
"6223453892842110664",
"435641772498947746481",
"32673132937421080986074",
"2613850634993686478885921",
"222177303974463350705303284"
] |
[
"nonn"
] | 35 | 0 | 2 |
[
"A001908",
"A320032"
] |
[
"M3677",
"N1500"
] |
N. J. A. Sloane
| 2020-01-17T10:36:50 |
oeisdata/seq/A001/A001908.seq
|
9f135f974fa8b6cd7b4956da94e8b845
|
A001909
|
a(n) = n*a(n-1) + (n-4)*a(n-2), a(2) = 0, a(3) = 1.
|
[
"0",
"1",
"4",
"21",
"134",
"1001",
"8544",
"81901",
"870274",
"10146321",
"128718044",
"1764651461",
"25992300894",
"409295679481",
"6860638482424",
"121951698034461",
"2291179503374234",
"45361686034627361",
"943892592746534964",
"20592893110265899381",
"470033715095287415734"
] |
[
"nonn"
] | 55 | 2 | 3 |
[
"A000153",
"A000255",
"A000261",
"A001909",
"A001910",
"A055790",
"A086764",
"A090010",
"A090012",
"A090016"
] |
[
"M3576",
"N1450"
] |
N. J. A. Sloane
| 2025-04-21T13:24:14 |
oeisdata/seq/A001/A001909.seq
|
0ee21ce278401cf3bfaac058b144f51d
|
A001910
|
a(n) = n*a(n-1) + (n-5)*a(n-2).
|
[
"0",
"1",
"5",
"31",
"227",
"1909",
"18089",
"190435",
"2203319",
"27772873",
"378673901",
"5551390471",
"87057596075",
"1453986832381",
"25762467303377",
"482626240281739",
"9530573107600319",
"197850855756232465",
"4307357140602486869",
"98125321641110663023",
"2334414826276390013171"
] |
[
"nonn"
] | 32 | 3 | 3 |
[
"A000153",
"A000255",
"A000261",
"A001909",
"A001910",
"A055790",
"A086764",
"A090012",
"A090016"
] |
[
"M3965",
"N1637"
] |
N. J. A. Sloane
| 2015-02-06T19:39:19 |
oeisdata/seq/A001/A001910.seq
|
059fa2131fec513b53db30e84117cb06
|
A001911
|
a(n) = Fibonacci(n+3) - 2.
|
[
"0",
"1",
"3",
"6",
"11",
"19",
"32",
"53",
"87",
"142",
"231",
"375",
"608",
"985",
"1595",
"2582",
"4179",
"6763",
"10944",
"17709",
"28655",
"46366",
"75023",
"121391",
"196416",
"317809",
"514227",
"832038",
"1346267",
"2178307",
"3524576",
"5702885",
"9227463",
"14930350",
"24157815",
"39088167",
"63245984"
] |
[
"nonn",
"easy",
"nice"
] | 181 | 0 | 3 |
[
"A000032",
"A000045",
"A000071",
"A001611",
"A001911",
"A006327",
"A011794",
"A101220",
"A104326",
"A108617",
"A157725",
"A157726",
"A157727",
"A157728",
"A157729",
"A165910",
"A167616",
"A181631",
"A226538",
"A261019",
"A372501"
] |
[
"M2546",
"N1007"
] |
N. J. A. Sloane
| 2025-06-30T21:12:00 |
oeisdata/seq/A001/A001911.seq
|
4f63b99336cade30286cf54cb143b7e1
|
A001912
|
Numbers k such that 4*k^2 + 1 is prime.
|
[
"1",
"2",
"3",
"5",
"7",
"8",
"10",
"12",
"13",
"18",
"20",
"27",
"28",
"33",
"37",
"42",
"45",
"47",
"55",
"58",
"60",
"62",
"63",
"65",
"67",
"73",
"75",
"78",
"80",
"85",
"88",
"90",
"92",
"102",
"103",
"105",
"112",
"115",
"118",
"120",
"125",
"128",
"130",
"132",
"135",
"140",
"142",
"150",
"153",
"157",
"163",
"170",
"175",
"192",
"193",
"198",
"200"
] |
[
"nonn",
"easy",
"nice"
] | 64 | 1 | 2 |
[
"A001912",
"A002496",
"A005574",
"A062325",
"A090693",
"A094550",
"A214517"
] |
[
"M0636",
"N0232"
] |
N. J. A. Sloane
| 2022-04-05T21:15:10 |
oeisdata/seq/A001/A001912.seq
|
a9d24ea7eddd8d9fc6dd5f67b5691596
|
A001913
|
Full reptend primes: primes with primitive root 10.
|
[
"7",
"17",
"19",
"23",
"29",
"47",
"59",
"61",
"97",
"109",
"113",
"131",
"149",
"167",
"179",
"181",
"193",
"223",
"229",
"233",
"257",
"263",
"269",
"313",
"337",
"367",
"379",
"383",
"389",
"419",
"433",
"461",
"487",
"491",
"499",
"503",
"509",
"541",
"571",
"577",
"593",
"619",
"647",
"659",
"701",
"709",
"727",
"743",
"811",
"821",
"823",
"857",
"863",
"887",
"937",
"941",
"953",
"971",
"977",
"983"
] |
[
"nonn",
"easy",
"nice"
] | 130 | 1 | 1 |
[
"A001122",
"A001913",
"A001914",
"A003277",
"A005596",
"A006883",
"A048296",
"A051626",
"A180340"
] |
[
"M4353",
"N1823"
] |
N. J. A. Sloane
| 2025-03-04T07:34:53 |
oeisdata/seq/A001/A001913.seq
|
0c0f8b39a6fba699bfcf522c17d091a0
|
A001914
|
Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.
|
[
"2",
"13",
"31",
"43",
"67",
"71",
"83",
"89",
"107",
"151",
"157",
"163",
"191",
"197",
"199",
"227",
"283",
"293",
"307",
"311",
"347",
"359",
"373",
"401",
"409",
"431",
"439",
"443",
"467",
"479",
"523",
"557",
"563",
"569",
"587",
"599",
"601",
"631",
"653",
"677",
"683",
"719",
"761",
"787",
"827",
"839",
"877",
"881",
"883",
"911",
"919",
"929",
"947",
"991"
] |
[
"nonn"
] | 23 | 1 | 1 |
[
"A000040",
"A001914",
"A002275",
"A003277",
"A071126"
] |
[
"M2940",
"N1183"
] |
N. J. A. Sloane
| 2018-09-18T04:48:33 |
oeisdata/seq/A001/A001914.seq
|
66f5f2957bc87fbd3ac258db9457c55e
|
A001915
|
Primes p such that the congruence 2^x == 3 (mod p) is solvable.
|
[
"2",
"5",
"11",
"13",
"19",
"23",
"29",
"37",
"47",
"53",
"59",
"61",
"67",
"71",
"83",
"97",
"101",
"107",
"131",
"139",
"149",
"163",
"167",
"173",
"179",
"181",
"191",
"193",
"197",
"211",
"227",
"239",
"263",
"269",
"293",
"307",
"311",
"313",
"317",
"347",
"349",
"359",
"373",
"379",
"383",
"389",
"409",
"419",
"421",
"431",
"443",
"461",
"467",
"479",
"491",
"499",
"503",
"509",
"523"
] |
[
"nonn",
"easy",
"nice"
] | 43 | 1 | 1 |
[
"A001915",
"A001916",
"A050259",
"A123988"
] |
[
"M3807",
"N1555"
] |
N. J. A. Sloane
| 2021-02-20T00:37:44 |
oeisdata/seq/A001/A001915.seq
|
fc36dad446afc3445c783686315e6278
|
A001916
|
Primes p such that the congruence 2^x = 5 (mod p) is solvable.
|
[
"2",
"3",
"11",
"13",
"19",
"29",
"37",
"41",
"53",
"59",
"61",
"67",
"71",
"79",
"83",
"101",
"107",
"131",
"139",
"149",
"163",
"173",
"179",
"181",
"191",
"197",
"199",
"211",
"227",
"239",
"251",
"269",
"271",
"293",
"311",
"317",
"347",
"349",
"359",
"373",
"379",
"389",
"401",
"409",
"419",
"421",
"443",
"449",
"461",
"467",
"479",
"491",
"509",
"521",
"523",
"541",
"547",
"557"
] |
[
"nonn"
] | 24 | 1 | 1 |
[
"A001915",
"A001916"
] |
[
"M4772",
"N2038"
] |
N. J. A. Sloane
| 2016-12-26T02:03:29 |
oeisdata/seq/A001/A001916.seq
|
79f09e7ac7a8a4dba68ecd87962c3db9
|
A001917
|
(p-1)/x, where p = prime(n) and x = ord(2,p), the smallest positive integer such that 2^x == 1 (mod p).
|
[
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"1",
"6",
"1",
"2",
"3",
"2",
"1",
"1",
"1",
"1",
"2",
"8",
"2",
"1",
"8",
"2",
"1",
"2",
"1",
"3",
"4",
"18",
"1",
"2",
"1",
"1",
"10",
"3",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"2",
"1",
"6",
"1",
"3",
"8",
"2",
"10",
"5",
"16",
"2",
"1",
"2",
"3",
"4",
"3",
"1",
"3",
"2",
"2",
"1",
"11",
"16",
"1",
"1",
"4",
"2",
"2",
"1",
"1",
"2",
"1",
"9",
"2",
"2",
"1",
"1",
"10",
"6",
"6",
"1",
"2",
"6",
"1",
"2",
"1",
"2",
"2",
"1",
"3",
"2",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2"
] |
[
"nonn",
"easy",
"nice"
] | 81 | 2 | 3 |
[
"A001122",
"A001133",
"A001134",
"A001135",
"A001136",
"A001917",
"A002323",
"A006694",
"A014664",
"A101208",
"A115591"
] |
[
"M0069",
"N0022"
] |
N. J. A. Sloane
| 2023-08-21T13:58:48 |
oeisdata/seq/A001/A001917.seq
|
02e1d42707a70b1f0b22d43c1f48b941
|
A001918
|
Least positive primitive root of n-th prime.
|
[
"1",
"2",
"2",
"3",
"2",
"2",
"3",
"2",
"5",
"2",
"3",
"2",
"6",
"3",
"5",
"2",
"2",
"2",
"2",
"7",
"5",
"3",
"2",
"3",
"5",
"2",
"5",
"2",
"6",
"3",
"3",
"2",
"3",
"2",
"2",
"6",
"5",
"2",
"5",
"2",
"2",
"2",
"19",
"5",
"2",
"3",
"2",
"3",
"2",
"6",
"3",
"7",
"7",
"6",
"3",
"5",
"2",
"6",
"5",
"3",
"3",
"2",
"5",
"17",
"10",
"2",
"3",
"10",
"2",
"2",
"3",
"7",
"6",
"2",
"2",
"5",
"2",
"5",
"3",
"21",
"2",
"2",
"7",
"5",
"15",
"2",
"3",
"13",
"2",
"3",
"2",
"13",
"3",
"2",
"7",
"5",
"2",
"3",
"2",
"2",
"2",
"2",
"2",
"3"
] |
[
"nonn",
"nice",
"easy"
] | 84 | 1 | 2 |
[
"A001918",
"A002233",
"A060749"
] |
[
"M0242",
"N0083"
] |
N. J. A. Sloane
| 2025-03-29T15:31:54 |
oeisdata/seq/A001/A001918.seq
|
351aefc3e4c1d55007d32a638cc301fa
|
A001919
|
Eighth column of quadrinomial coefficients.
|
[
"6",
"40",
"155",
"456",
"1128",
"2472",
"4950",
"9240",
"16302",
"27456",
"44473",
"69680",
"106080",
"157488",
"228684",
"325584",
"455430",
"627000",
"850839",
"1139512",
"1507880",
"1973400",
"2556450",
"3280680",
"4173390",
"5265936",
"6594165",
"8198880",
"10126336",
"12428768",
"15164952",
"18400800",
"22209990"
] |
[
"nonn",
"easy"
] | 51 | 3 | 1 | null |
[
"M4234",
"N1769"
] |
N. J. A. Sloane
| 2022-04-13T13:25:16 |
oeisdata/seq/A001/A001919.seq
|
6e4c653a264323f543f5db9b98ac05ef
|
A001920
|
Expansion of 1/(1+759*x^2+2576*x^3+759*x^4+x^6).
|
[
"1",
"0",
"-759",
"-2576",
"575322",
"3910368",
"-429457542",
"-4448043600",
"315448497771",
"4479379753856",
"-227641291795533",
"-4209068502252768",
"161001433246525844",
"3777687116090010816",
"-111184747947285673452",
"-3278809534641538686432"
] |
[
"sign",
"easy"
] | 17 | 0 | 3 | null | null |
N. J. A. Sloane
| 2024-11-07T17:03:11 |
oeisdata/seq/A001/A001920.seq
|
48a1579a5cbd895dde53e3e7b5820274
|
A001921
|
a(n) = 14*a(n-1) - a(n-2) + 6 for n>1, a(0)=0, a(1)=7.
|
[
"0",
"7",
"104",
"1455",
"20272",
"282359",
"3932760",
"54776287",
"762935264",
"10626317415",
"148005508552",
"2061450802319",
"28712305723920",
"399910829332567",
"5570039304932024",
"77580639439715775",
"1080558912851088832",
"15050244140475527879",
"209622859053806301480"
] |
[
"nonn",
"easy"
] | 74 | 0 | 2 |
[
"A000217",
"A001570",
"A001652",
"A001921",
"A001922",
"A006051",
"A006451",
"A129556",
"A233450"
] |
[
"M4455",
"N1885"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A001/A001921.seq
|
192b504d5d2a7360a14be7710a390e20
|
A001922
|
Numbers k such that 3*k^2 - 3*k + 1 is both a square (A000290) and a centered hexagonal number (A003215).
|
[
"1",
"8",
"105",
"1456",
"20273",
"282360",
"3932761",
"54776288",
"762935265",
"10626317416",
"148005508553",
"2061450802320",
"28712305723921",
"399910829332568",
"5570039304932025",
"77580639439715776",
"1080558912851088833",
"15050244140475527880",
"209622859053806301481"
] |
[
"nonn",
"easy",
"changed"
] | 85 | 0 | 2 |
[
"A001075",
"A001353",
"A001570",
"A001844",
"A001921",
"A001922",
"A003215",
"A005448",
"A006051",
"A016754",
"A076139",
"A156712"
] |
[
"M4569",
"N1946"
] |
N. J. A. Sloane
| 2025-07-15T00:38:41 |
oeisdata/seq/A001/A001922.seq
|
d56a54d22694e105972727356c1486b8
|
A001923
|
a(n) = Sum_{k=1..n} k^k.
|
[
"0",
"1",
"5",
"32",
"288",
"3413",
"50069",
"873612",
"17650828",
"405071317",
"10405071317",
"295716741928",
"9211817190184",
"312086923782437",
"11424093749340453",
"449317984130199828",
"18896062057839751444",
"846136323944176515621"
] |
[
"nonn",
"easy",
"nice"
] | 103 | 0 | 3 |
[
"A000312",
"A001923",
"A002109",
"A060946",
"A062815",
"A062970",
"A073825",
"A117887"
] |
[
"M3968",
"N1639"
] |
N. J. A. Sloane
| 2025-01-05T19:51:32 |
oeisdata/seq/A001/A001923.seq
|
dc99d997bafd20408f037fe7991d2f71
|
A001924
|
Apply partial sum operator twice to Fibonacci numbers.
|
[
"0",
"1",
"3",
"7",
"14",
"26",
"46",
"79",
"133",
"221",
"364",
"596",
"972",
"1581",
"2567",
"4163",
"6746",
"10926",
"17690",
"28635",
"46345",
"75001",
"121368",
"196392",
"317784",
"514201",
"832011",
"1346239",
"2178278",
"3524546",
"5702854",
"9227431",
"14930317",
"24157781",
"39088132",
"63245948",
"102334116",
"165580101"
] |
[
"nonn",
"easy",
"nice"
] | 203 | 0 | 3 |
[
"A000045",
"A001891",
"A001924",
"A011794",
"A014162",
"A023548",
"A039834",
"A065220",
"A077880",
"A122595",
"A129696",
"A133640",
"A141289"
] |
[
"M2645",
"N1053"
] |
N. J. A. Sloane
| 2025-04-28T09:02:19 |
oeisdata/seq/A001/A001924.seq
|
299eab06708c9d9281941a3c8aca836a
|
A001925
|
From rook polynomials.
|
[
"1",
"6",
"22",
"64",
"162",
"374",
"809",
"1668",
"3316",
"6408",
"12108",
"22468",
"41081",
"74202",
"132666",
"235160",
"413790",
"723530",
"1258225",
"2177640",
"3753096",
"6444336",
"11028792",
"18818664",
"32024977",
"54367374",
"92094334",
"155688208",
"262711866",
"442556798",
"744355673",
"1250157228"
] |
[
"nonn"
] | 33 | 0 | 2 |
[
"A001925",
"A002940"
] |
[
"M4151",
"N1724"
] |
N. J. A. Sloane
| 2022-04-13T13:25:16 |
oeisdata/seq/A001/A001925.seq
|
5d2b1e360c044c858045e53f77931d6e
|
A001926
|
G.f.: (1+x)^2/[(1-x)^4(1-x-x^2)^3].
|
[
"1",
"9",
"46",
"177",
"571",
"1632",
"4270",
"10446",
"24244",
"53942",
"115954",
"242240",
"494087",
"987503",
"1939634",
"3753007",
"7167461",
"13532608",
"25293964",
"46856332",
"86110792",
"157125052",
"284866900",
"513470464",
"920659517",
"1642844485",
"2918680214",
"5164483453",
"9104522495",
"15995633440"
] |
[
"nonn"
] | 32 | 0 | 2 |
[
"A001926",
"A002941"
] |
[
"M4628",
"N1978"
] |
N. J. A. Sloane
| 2022-04-30T16:58:36 |
oeisdata/seq/A001/A001926.seq
|
bd88c97ff90a1736ea89d2c0e6aa3804
|
A001927
|
Number of connected partially ordered sets with n labeled points.
|
[
"1",
"1",
"2",
"12",
"146",
"3060",
"101642",
"5106612",
"377403266",
"40299722580",
"6138497261882",
"1320327172853172",
"397571105288091506",
"166330355795371103700",
"96036130723851671469482",
"76070282980382554147600692",
"82226869197428315925408327266",
"120722306604121583767045993825620",
"239727397782668638856762574296226842"
] |
[
"nonn",
"nice",
"hard",
"changed"
] | 56 | 0 | 3 |
[
"A000110",
"A000112",
"A000608",
"A000798",
"A001035",
"A001927",
"A001929",
"A006056",
"A006057",
"A006058",
"A006059",
"A066303",
"A342501"
] |
[
"M2043",
"N0809"
] |
N. J. A. Sloane
| 2025-07-08T16:27:15 |
oeisdata/seq/A001/A001927.seq
|
ef81f8e8cef841965cad0eb172400d60
|
A001928
|
Number of connected topologies with n unlabeled nodes.
|
[
"1",
"1",
"2",
"6",
"21",
"94",
"512",
"3485",
"29515",
"314474",
"4255727",
"73831813",
"1653083021",
"47941962135",
"1803010446411",
"87882300251730",
"5543501326580737"
] |
[
"nonn",
"more"
] | 43 | 0 | 3 |
[
"A001928",
"A001929",
"A001930"
] |
[
"M1655",
"N0648"
] |
N. J. A. Sloane
| 2021-12-24T00:34:03 |
oeisdata/seq/A001/A001928.seq
|
a2f6e0d5302a308fec8f0a3a26f885e2
|
A001929
|
Number of connected topologies on n labeled points.
|
[
"1",
"1",
"3",
"19",
"233",
"4851",
"158175",
"7724333",
"550898367",
"56536880923",
"8267519506789",
"1709320029453719",
"496139872875425839",
"200807248677750187825",
"112602879608997769049739",
"86955243134629606109442219",
"91962123875462441868790125305",
"132524871920295877733718959290203",
"259048612476248175744581063815546423"
] |
[
"nonn",
"nice"
] | 43 | 0 | 3 |
[
"A000110",
"A000798",
"A001035",
"A001927",
"A001928",
"A001929",
"A001930",
"A006056",
"A006057",
"A006058",
"A006059"
] |
[
"M3070",
"N1245"
] |
N. J. A. Sloane
| 2018-08-30T15:45:01 |
oeisdata/seq/A001/A001929.seq
|
533d0349bdf70c753987e08f0e125d9e
|
A001930
|
Number of topologies, or transitive digraphs with n unlabeled nodes.
|
[
"1",
"1",
"3",
"9",
"33",
"139",
"718",
"4535",
"35979",
"363083",
"4717687",
"79501654",
"1744252509",
"49872339897",
"1856792610995",
"89847422244493",
"5637294117525695"
] |
[
"nonn",
"hard",
"more",
"nice"
] | 101 | 0 | 3 |
[
"A000112",
"A000612",
"A000798",
"A001035",
"A001928",
"A001929",
"A001930",
"A003180",
"A006057",
"A108798",
"A108800",
"A193674",
"A306445",
"A326876",
"A326878",
"A326882",
"A326898"
] |
[
"M2817",
"N1133"
] |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001930.seq
|
fc4c8d1a521d3eac04a6be47fe4be693
|
A001931
|
Number of fixed 3-dimensional polycubes with n cells; lattice animals in the simple cubic lattice (6 nearest neighbors), face-connected cubes.
|
[
"1",
"3",
"15",
"86",
"534",
"3481",
"23502",
"162913",
"1152870",
"8294738",
"60494549",
"446205905",
"3322769321",
"24946773111",
"188625900446",
"1435074454755",
"10977812452428",
"84384157287999",
"651459315795897",
"5049008190434659",
"39269513463794006",
"306405169166373418"
] |
[
"nonn",
"nice",
"more"
] | 101 | 1 | 2 |
[
"A000162",
"A001420",
"A001931",
"A038119",
"A151830",
"A151832",
"A151833",
"A151834",
"A151835",
"A366767"
] |
[
"M2996",
"N1213"
] |
N. J. A. Sloane
| 2024-02-08T01:41:05 |
oeisdata/seq/A001/A001931.seq
|
ab6fb104843a4f89eae5ed39b43aae4e
|
A001932
|
Sum of Fibonacci (A000045) and Pell (A000129) numbers.
|
[
"0",
"2",
"3",
"7",
"15",
"34",
"78",
"182",
"429",
"1019",
"2433",
"5830",
"14004",
"33694",
"81159",
"195635",
"471819",
"1138286",
"2746794",
"6629290",
"16001193",
"38624911",
"93240069",
"225087338",
"543386088",
"1311813146",
"3166937355",
"7645566463",
"18457873863",
"44560996378",
"107579352390",
"259718869118"
] |
[
"nonn",
"easy"
] | 67 | 0 | 2 | null |
[
"M0844",
"N0319"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A001/A001932.seq
|
6726497a0d9822aa1dcebb134d43d07b
|
A001933
|
Number of chessboard polyominoes with n squares.
|
[
"2",
"1",
"4",
"7",
"24",
"62",
"216",
"710",
"2570",
"9215",
"34146",
"126853",
"477182",
"1802673",
"6853152",
"26153758",
"100215818",
"385226201",
"1485248464",
"5741275753",
"22246121356",
"86383454582",
"336094015456",
"1309998396933",
"5114454089528",
"19998173763831",
"78306021876974",
"307022186132259",
"1205243906123956",
"4736694016531135"
] |
[
"hard",
"nonn"
] | 59 | 1 | 1 |
[
"A000105",
"A001071",
"A001933",
"A121198",
"A234006",
"A234007",
"A234008"
] |
[
"M0171",
"N0066"
] |
N. J. A. Sloane
| 2024-12-23T14:53:41 |
oeisdata/seq/A001/A001933.seq
|
daa289291a783668be9637586de90d06
|
A001934
|
Expansion of 1/theta_4(q)^2 in powers of q.
|
[
"1",
"4",
"12",
"32",
"76",
"168",
"352",
"704",
"1356",
"2532",
"4600",
"8160",
"14176",
"24168",
"40512",
"66880",
"108876",
"174984",
"277932",
"436640",
"679032",
"1046016",
"1597088",
"2418240",
"3632992",
"5417708",
"8022840",
"11802176",
"17252928",
"25070568",
"36223424",
"52053760",
"74414412"
] |
[
"nonn",
"easy"
] | 96 | 0 | 2 |
[
"A000122",
"A000203",
"A001934",
"A002318",
"A002513",
"A004403",
"A004404",
"A004425",
"A015128"
] |
[
"M3443",
"N1397"
] |
N. J. A. Sloane, Simon Plouffe
| 2025-07-02T16:01:54 |
oeisdata/seq/A001/A001934.seq
|
4b629f9510bfaa02b622444f4431690a
|
A001935
|
Number of partitions with no even part repeated; partitions of n in which no parts are multiples of 4.
|
[
"1",
"1",
"2",
"3",
"4",
"6",
"9",
"12",
"16",
"22",
"29",
"38",
"50",
"64",
"82",
"105",
"132",
"166",
"208",
"258",
"320",
"395",
"484",
"592",
"722",
"876",
"1060",
"1280",
"1539",
"1846",
"2210",
"2636",
"3138",
"3728",
"4416",
"5222",
"6163",
"7256",
"8528",
"10006",
"11716",
"13696",
"15986",
"18624",
"21666",
"25169",
"29190",
"33808",
"39104",
"45164"
] |
[
"nonn",
"easy",
"nice"
] | 177 | 0 | 3 |
[
"A000009",
"A000041",
"A000726",
"A001935",
"A001936",
"A010054",
"A035959",
"A035985",
"A042968",
"A061198",
"A061199",
"A070048",
"A081055",
"A081056",
"A082303",
"A083365",
"A098491",
"A098492",
"A104502",
"A174715",
"A219601",
"A261775",
"A261776",
"A328545",
"A328546"
] |
[
"M0566",
"N0204"
] |
N. J. A. Sloane, Simon Plouffe, Robert G. Wilson v
| 2025-07-02T16:01:54 |
oeisdata/seq/A001/A001935.seq
|
404a87d9ee1809ac45988c58d0a9f6bc
|
A001936
|
Expansion of q^(-1/4) * (eta(q^4) / eta(q))^2 in powers of q.
|
[
"1",
"2",
"5",
"10",
"18",
"32",
"55",
"90",
"144",
"226",
"346",
"522",
"777",
"1138",
"1648",
"2362",
"3348",
"4704",
"6554",
"9056",
"12425",
"16932",
"22922",
"30848",
"41282",
"54946",
"72768",
"95914",
"125842",
"164402",
"213901",
"277204",
"357904",
"460448",
"590330",
"754368",
"960948",
"1220370",
"1545306"
] |
[
"nonn",
"easy"
] | 86 | 0 | 2 |
[
"A001935",
"A001936",
"A022567",
"A022568",
"A079006",
"A082304",
"A098613",
"A127391",
"A127392",
"A210656",
"A263002",
"A328547",
"A328548",
"A333374"
] |
[
"M1372",
"N0532"
] |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001936.seq
|
638b7dafcbfaa7c9f4663b8c158377a2
|
A001937
|
Expansion of (psi(x^2) / psi(-x))^3 in powers of x where psi() is a Ramanujan theta function.
|
[
"1",
"3",
"9",
"22",
"48",
"99",
"194",
"363",
"657",
"1155",
"1977",
"3312",
"5443",
"8787",
"13968",
"21894",
"33873",
"51795",
"78345",
"117312",
"174033",
"255945",
"373353",
"540486",
"776848",
"1109040",
"1573209",
"2218198",
"3109713",
"4335840",
"6014123",
"8300811",
"11402928",
"15593702",
"21232521",
"28790667",
"38884082"
] |
[
"nonn"
] | 44 | 0 | 2 |
[
"A001935",
"A001936",
"A001937",
"A001938",
"A001939",
"A001940",
"A001941",
"A079006",
"A083365",
"A093160"
] |
[
"M2785",
"N1120"
] |
N. J. A. Sloane, Simon Plouffe
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001937.seq
|
4cb784b6a1cf9235abedecda07bf8e3f
|
A001938
|
Expansion of k/(4*q^(1/2)) in powers of q, where k defined by sqrt(k) = theta_2(0, q)/theta_3(0, q).
|
[
"1",
"-4",
"14",
"-40",
"101",
"-236",
"518",
"-1080",
"2162",
"-4180",
"7840",
"-14328",
"25591",
"-44776",
"76918",
"-129952",
"216240",
"-354864",
"574958",
"-920600",
"1457946",
"-2285452",
"3548550",
"-5460592",
"8332425",
"-12614088",
"18953310",
"-28276968",
"41904208",
"-61702876",
"90304598",
"-131399624"
] |
[
"sign",
"easy",
"nice"
] | 63 | 0 | 2 |
[
"A000122",
"A000700",
"A001936",
"A001938",
"A010054",
"A079006",
"A093160",
"A121373",
"A127393",
"A127931",
"A127932",
"A139820"
] |
[
"M3475",
"N1412"
] |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001938.seq
|
95d429fc181cfbb85b15e8df125fed2c
|
A001939
|
Expansion of (psi(-x) / phi(-x))^5 in powers of x where phi(), psi() are Ramanujan theta functions.
|
[
"1",
"5",
"20",
"65",
"185",
"481",
"1165",
"2665",
"5820",
"12220",
"24802",
"48880",
"93865",
"176125",
"323685",
"583798",
"1035060",
"1806600",
"3108085",
"5276305",
"8846884",
"14663645",
"24044285",
"39029560",
"62755345",
"100004806",
"158022900",
"247710570",
"385366265",
"595212280",
"913040649",
"1391449780"
] |
[
"nonn",
"easy"
] | 46 | 0 | 2 |
[
"A000122",
"A000700",
"A001939",
"A010054",
"A121373",
"A195861"
] |
[
"M3898",
"N1599"
] |
N. J. A. Sloane, Simon Plouffe
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001939.seq
|
721b6faa2b04d46716e267495e1549fb
|
A001940
|
Absolute value of coefficients of an elliptic function.
|
[
"1",
"6",
"27",
"98",
"309",
"882",
"2330",
"5784",
"13644",
"30826",
"67107",
"141444",
"289746",
"578646",
"1129527",
"2159774",
"4052721",
"7474806",
"13569463",
"24274716",
"42838245",
"74644794",
"128533884",
"218881098",
"368859591",
"615513678",
"1017596115",
"1667593666",
"2710062756",
"4369417452"
] |
[
"nonn",
"easy"
] | 28 | 0 | 2 |
[
"A001935",
"A001936",
"A001937",
"A001939",
"A001940",
"A001941",
"A092877",
"A093160"
] |
[
"M4173",
"N1737"
] |
N. J. A. Sloane, Simon Plouffe
| 2017-12-04T09:17:13 |
oeisdata/seq/A001/A001940.seq
|
592fa2525f0ed09e1d226d0acec7d418
|
A001941
|
Absolute values of coefficients of an elliptic function.
|
[
"1",
"7",
"35",
"140",
"483",
"1498",
"4277",
"11425",
"28889",
"69734",
"161735",
"362271",
"786877",
"1662927",
"3428770",
"6913760",
"13660346",
"26492361",
"50504755",
"94766875",
"175221109",
"319564227",
"575387295",
"1023624280",
"1800577849",
"3133695747",
"5399228149",
"9214458260",
"15584195428"
] |
[
"nonn"
] | 26 | 0 | 2 |
[
"A001935",
"A001936",
"A001937",
"A001939",
"A001940",
"A001941",
"A092877",
"A093160"
] |
[
"M4411",
"N1864"
] |
N. J. A. Sloane, Simon Plouffe
| 2017-12-04T09:17:21 |
oeisdata/seq/A001/A001941.seq
|
f16e38b90c20f2a5b79697830e9e80b6
|
A001942
|
Expansion of reciprocal of theta series of Leech lattice.
|
[
"1",
"0",
"-196560",
"-16773120",
"38237799600",
"6589219553280",
"-7156481189457600",
"-1928958160910376960",
"1281020641484922702000",
"496393397255370269491200",
"-216626064507656630386166880",
"-118257112035536800684700160000"
] |
[
"sign"
] | 16 | 0 | 3 |
[
"A001942",
"A008408"
] | null |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001942.seq
|
7d19a50f2a22f6f988de2f2c7803279a
|
A001943
|
Expansion of reciprocal of theta series of E_8 lattice.
|
[
"1",
"-240",
"55440",
"-12793920",
"2952385680",
"-681306078240",
"157221316739520",
"-36281112432850560",
"8372395974330234000",
"-1932052510261208053680",
"445849302141400152457440",
"-102886230661038692118348480"
] |
[
"sign"
] | 16 | 0 | 2 |
[
"A001943",
"A004009"
] | null |
N. J. A. Sloane
| 2018-03-05T06:16:28 |
oeisdata/seq/A001/A001943.seq
|
8c1804d8d8fb5d19f4a534f9dc227a89
|
A001944
|
Numbers that are the sum of 4 distinct squares: of form w^2 + x^2 + y^2 + z^2 with 0 <= w < x < y < z.
|
[
"14",
"21",
"26",
"29",
"30",
"35",
"38",
"39",
"41",
"42",
"45",
"46",
"49",
"50",
"51",
"53",
"54",
"56",
"57",
"59",
"61",
"62",
"63",
"65",
"66",
"69",
"70",
"71",
"74",
"75",
"77",
"78",
"79",
"81",
"83",
"84",
"85",
"86",
"87",
"89",
"90",
"91",
"93",
"94",
"95",
"98",
"99",
"101",
"102",
"104",
"105",
"106",
"107",
"109",
"110",
"111",
"113",
"114",
"115",
"116",
"117"
] |
[
"nonn",
"easy"
] | 15 | 1 | 1 |
[
"A001944",
"A001948",
"A001974",
"A001983",
"A001995"
] | null |
N. J. A. Sloane
| 2022-02-04T00:44:08 |
oeisdata/seq/A001/A001944.seq
|
3c65f77aa9f0176b88e1986e60a2b054
|
A001945
|
a(n+6) = -a(n+5) + a(n+4) + 3a(n+3) + a(n+2) - a(n+1) - a(n). a(n) = sign(n) if abs(n)<=3.
|
[
"0",
"1",
"1",
"1",
"5",
"1",
"7",
"8",
"5",
"19",
"11",
"23",
"35",
"27",
"64",
"61",
"85",
"137",
"133",
"229",
"275",
"344",
"529",
"599",
"875",
"1151",
"1431",
"2071",
"2560",
"3481",
"4697",
"5953",
"8245",
"10649",
"14111",
"19048",
"24605",
"33227",
"43739",
"57591",
"77275",
"101107",
"134848",
"178709",
"235405",
"314089",
"413909"
] |
[
"nonn",
"nice",
"easy"
] | 85 | 0 | 5 |
[
"A001351",
"A001608",
"A001945",
"A078712",
"A104499"
] |
[
"M3730",
"N1525"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A001/A001945.seq
|
f52a666571369d76677d33a0035aa92c
|
A001946
|
a(n) = 11*a(n-1) + a(n-2).
|
[
"2",
"11",
"123",
"1364",
"15127",
"167761",
"1860498",
"20633239",
"228826127",
"2537720636",
"28143753123",
"312119004989",
"3461452808002",
"38388099893011",
"425730551631123",
"4721424167835364",
"52361396397820127",
"580696784543856761",
"6440026026380244498",
"71420983074726546239"
] |
[
"easy",
"nonn"
] | 60 | 0 | 1 |
[
"A000032",
"A000045",
"A001946",
"A121171",
"A124296",
"A124297"
] |
[
"M2009",
"N0794"
] |
N. J. A. Sloane, Simon Plouffe
| 2025-01-18T21:56:57 |
oeisdata/seq/A001/A001946.seq
|
60561e664fef0164773f1156de3e13c6
|
A001947
|
a(n) = Lucas(5*n+2).
|
[
"3",
"29",
"322",
"3571",
"39603",
"439204",
"4870847",
"54018521",
"599074578",
"6643838879",
"73681302247",
"817138163596",
"9062201101803",
"100501350283429",
"1114577054219522",
"12360848946698171",
"137083915467899403",
"1520283919093591604",
"16860207025497407047",
"186982561199565069121"
] |
[
"nonn",
"easy"
] | 56 | 0 | 1 | null |
[
"M3120",
"N1265"
] |
N. J. A. Sloane
| 2022-09-08T08:44:29 |
oeisdata/seq/A001/A001947.seq
|
b7fe5e2d562a71ba4711d28fc61840cd
|
A001948
|
These numbers when multiplied by all powers of 4 give the numbers that are not the sums of 4 distinct squares.
|
[
"1",
"2",
"3",
"5",
"6",
"7",
"9",
"10",
"11",
"13",
"15",
"17",
"18",
"19",
"22",
"23",
"25",
"27",
"31",
"33",
"34",
"37",
"43",
"47",
"55",
"58",
"67",
"73",
"82",
"97",
"103"
] |
[
"nonn",
"fini",
"full"
] | 23 | 1 | 2 |
[
"A001944",
"A001948",
"A004437"
] | null |
N. J. A. Sloane, Dan Hoey
| 2017-10-03T03:59:04 |
oeisdata/seq/A001/A001948.seq
|
802aa76b5331a9ebc517c0474c4f352c
|
A001949
|
Solutions of a fifth-order probability difference equation.
|
[
"0",
"0",
"0",
"0",
"0",
"1",
"2",
"4",
"8",
"16",
"32",
"63",
"124",
"244",
"480",
"944",
"1856",
"3649",
"7174",
"14104",
"27728",
"54512",
"107168",
"210687",
"414200",
"814296",
"1600864",
"3147216",
"6187264",
"12163841",
"23913482",
"47012668",
"92424472",
"181701728",
"357216192",
"702268543",
"1380623604",
"2714234540"
] |
[
"nonn",
"easy"
] | 85 | 0 | 7 |
[
"A001591",
"A001949",
"A141020",
"A141021",
"A172119"
] |
[
"M1127",
"N0430"
] |
N. J. A. Sloane
| 2025-03-28T11:28:14 |
oeisdata/seq/A001/A001949.seq
|
bc827a80fd62c65945d776e3135f2a95
|
A001950
|
Upper Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi^2), where phi = (1+sqrt(5))/2.
|
[
"2",
"5",
"7",
"10",
"13",
"15",
"18",
"20",
"23",
"26",
"28",
"31",
"34",
"36",
"39",
"41",
"44",
"47",
"49",
"52",
"54",
"57",
"60",
"62",
"65",
"68",
"70",
"73",
"75",
"78",
"81",
"83",
"86",
"89",
"91",
"94",
"96",
"99",
"102",
"104",
"107",
"109",
"112",
"115",
"117",
"120",
"123",
"125",
"128",
"130",
"133",
"136",
"138",
"141",
"143",
"146",
"149",
"151",
"154",
"157"
] |
[
"nonn",
"easy",
"nice"
] | 261 | 1 | 1 |
[
"A000201",
"A001030",
"A001468",
"A001622",
"A001950",
"A001962",
"A001966",
"A002251",
"A003622",
"A003623",
"A003842",
"A003849",
"A004641",
"A004919",
"A004976",
"A005614",
"A014417",
"A014675",
"A022342",
"A026242",
"A026352",
"A035336",
"A066096",
"A076662",
"A088462",
"A096270",
"A101864",
"A114986",
"A124841",
"A329825"
] |
[
"M1332",
"N0509"
] |
N. J. A. Sloane
| 2025-04-18T03:19:05 |
oeisdata/seq/A001/A001950.seq
|
f275ce58d12db97fa55eb61ae2f1bcf4
|
A001951
|
A Beatty sequence: a(n) = floor(n*sqrt(2)).
|
[
"0",
"1",
"2",
"4",
"5",
"7",
"8",
"9",
"11",
"12",
"14",
"15",
"16",
"18",
"19",
"21",
"22",
"24",
"25",
"26",
"28",
"29",
"31",
"32",
"33",
"35",
"36",
"38",
"39",
"41",
"42",
"43",
"45",
"46",
"48",
"49",
"50",
"52",
"53",
"55",
"56",
"57",
"59",
"60",
"62",
"63",
"65",
"66",
"67",
"69",
"70",
"72",
"73",
"74",
"76",
"77",
"79",
"80",
"82",
"83",
"84",
"86",
"87",
"89",
"90",
"91",
"93",
"94",
"96",
"97",
"98",
"100"
] |
[
"nonn",
"nice",
"easy"
] | 201 | 0 | 3 |
[
"A001951",
"A001952",
"A003151",
"A003152",
"A006337",
"A022342",
"A022842",
"A026250",
"A080763",
"A080764",
"A082844",
"A094077",
"A097509",
"A103341",
"A159684",
"A188037",
"A194102",
"A245219",
"A276862",
"A342281"
] |
[
"M0955",
"N0356"
] |
N. J. A. Sloane
| 2025-06-02T16:05:08 |
oeisdata/seq/A001/A001951.seq
|
a32009068921501e0148710644abfea2
|
A001952
|
A Beatty sequence: a(n) = floor(n*(2 + sqrt(2))).
|
[
"3",
"6",
"10",
"13",
"17",
"20",
"23",
"27",
"30",
"34",
"37",
"40",
"44",
"47",
"51",
"54",
"58",
"61",
"64",
"68",
"71",
"75",
"78",
"81",
"85",
"88",
"92",
"95",
"99",
"102",
"105",
"109",
"112",
"116",
"119",
"122",
"126",
"129",
"133",
"136",
"139",
"143",
"146",
"150",
"153",
"157",
"160",
"163",
"167",
"170",
"174",
"177",
"180",
"184",
"187",
"191",
"194",
"198"
] |
[
"nonn",
"easy",
"nice"
] | 73 | 1 | 1 |
[
"A001951",
"A001952",
"A003151",
"A003152",
"A006337",
"A026250",
"A080763",
"A080764",
"A082844",
"A094077",
"A097509",
"A159684",
"A187393",
"A188037",
"A245219",
"A276862",
"A342280"
] |
[
"M2534",
"N1001"
] |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001952.seq
|
4c07c7337d980b963b96f6346f5a02c8
|
A001953
|
a(n) = floor((n + 1/2) * sqrt(2)).
|
[
"0",
"2",
"3",
"4",
"6",
"7",
"9",
"10",
"12",
"13",
"14",
"16",
"17",
"19",
"20",
"21",
"23",
"24",
"26",
"27",
"28",
"30",
"31",
"33",
"34",
"36",
"37",
"38",
"40",
"41",
"43",
"44",
"45",
"47",
"48",
"50",
"51",
"53",
"54",
"55",
"57",
"58",
"60",
"61",
"62",
"64",
"65",
"67",
"68",
"70",
"71",
"72",
"74",
"75",
"77",
"78",
"79",
"81",
"82",
"84",
"85",
"86",
"88",
"89",
"91",
"92",
"94",
"95"
] |
[
"nonn"
] | 98 | 0 | 2 |
[
"A000217",
"A001108",
"A001953",
"A001954",
"A136119"
] |
[
"M0543",
"N0193"
] |
N. J. A. Sloane
| 2022-09-08T08:44:29 |
oeisdata/seq/A001/A001953.seq
|
3081cbfc5ddf58c2a3d3116ac0152078
|
A001954
|
a(n) = floor((n+1/2)*(2+sqrt(2))); winning positions in the 2-Wythoff game.
|
[
"1",
"5",
"8",
"11",
"15",
"18",
"22",
"25",
"29",
"32",
"35",
"39",
"42",
"46",
"49",
"52",
"56",
"59",
"63",
"66",
"69",
"73",
"76",
"80",
"83",
"87",
"90",
"93",
"97",
"100",
"104",
"107",
"110",
"114",
"117",
"121",
"124",
"128",
"131",
"134",
"138",
"141",
"145",
"148",
"151",
"155",
"158",
"162",
"165",
"169",
"172",
"175",
"179",
"182",
"186",
"189",
"192",
"196",
"199"
] |
[
"nonn"
] | 62 | 0 | 2 |
[
"A001953",
"A001954",
"A003152"
] |
[
"M3774",
"N1539"
] |
N. J. A. Sloane
| 2022-09-08T08:44:29 |
oeisdata/seq/A001/A001954.seq
|
79d93ffcd3c956fbf58902c7862e0363
|
A001955
|
Beatty sequence of 1 + 1/sqrt(11).
|
[
"1",
"2",
"3",
"5",
"6",
"7",
"9",
"10",
"11",
"13",
"14",
"15",
"16",
"18",
"19",
"20",
"22",
"23",
"24",
"26",
"27",
"28",
"29",
"31",
"32",
"33",
"35",
"36",
"37",
"39",
"40",
"41",
"42",
"44",
"45",
"46",
"48",
"49",
"50",
"52",
"53",
"54",
"55",
"57",
"58",
"59",
"61",
"62",
"63",
"65",
"66",
"67",
"68",
"70",
"71",
"72",
"74",
"75",
"76",
"78",
"79",
"80",
"81",
"83",
"84",
"85",
"87",
"88"
] |
[
"nonn"
] | 28 | 1 | 2 | null |
[
"M0615",
"N0225"
] |
N. J. A. Sloane
| 2024-07-30T04:19:41 |
oeisdata/seq/A001/A001955.seq
|
4de8ee00395dd0933507831bf16a16ea
|
A001956
|
Beatty sequence of (5+sqrt(13))/2.
|
[
"4",
"8",
"12",
"17",
"21",
"25",
"30",
"34",
"38",
"43",
"47",
"51",
"55",
"60",
"64",
"68",
"73",
"77",
"81",
"86",
"90",
"94",
"98",
"103",
"107",
"111",
"116",
"120",
"124",
"129",
"133",
"137",
"141",
"146",
"150",
"154",
"159",
"163",
"167",
"172",
"176",
"180",
"185",
"189",
"193",
"197",
"202",
"206",
"210",
"215",
"219",
"223",
"228",
"232",
"236",
"240",
"245",
"249"
] |
[
"nonn"
] | 28 | 1 | 1 |
[
"A001956",
"A184117",
"A184480",
"A184482"
] |
[
"M3327",
"N1338"
] |
N. J. A. Sloane
| 2015-08-02T22:18:24 |
oeisdata/seq/A001/A001956.seq
|
ce81c3120e83d96662c6e82840e84f9b
|
A001957
|
u-pile positions in the 3-Wythoff game with i=1.
|
[
"0",
"1",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"12",
"13",
"14",
"16",
"17",
"18",
"19",
"21",
"22",
"23",
"25",
"26",
"27",
"29",
"30",
"31",
"33",
"34",
"35",
"36",
"38",
"39",
"40",
"42",
"43",
"44",
"46",
"47",
"48",
"49",
"51",
"52",
"53",
"55",
"56",
"57",
"59",
"60",
"61",
"62",
"64",
"65",
"66",
"68",
"69",
"70",
"72",
"73",
"74",
"75",
"77",
"78",
"79",
"81",
"82",
"83",
"85",
"86",
"87"
] |
[
"nonn",
"easy"
] | 36 | 0 | 3 |
[
"A001954",
"A001957",
"A001958",
"A001960",
"A001963",
"A001968"
] |
[
"M2302",
"N0908"
] |
N. J. A. Sloane
| 2021-12-27T10:46:34 |
oeisdata/seq/A001/A001957.seq
|
d04d53aeb9e41af21f5fc4f46c85cdf0
|
A001958
|
v-pile numbers of the 3-Wythoff game with i=1.
|
[
"1",
"5",
"10",
"14",
"18",
"22",
"27",
"31",
"35",
"40",
"44",
"48",
"53",
"57",
"61",
"65",
"70",
"74",
"78",
"83",
"87",
"91",
"96",
"100",
"104",
"109",
"113",
"117",
"121",
"126",
"130",
"134",
"139",
"143",
"147",
"152",
"156",
"160",
"164",
"169",
"173",
"177",
"182",
"186",
"190",
"195",
"199",
"203",
"207",
"212",
"216",
"220",
"225",
"229",
"233",
"238",
"242",
"246"
] |
[
"nonn",
"easy"
] | 21 | 0 | 2 | null |
[
"M3794",
"N1547"
] |
N. J. A. Sloane
| 2022-02-04T00:44:01 |
oeisdata/seq/A001/A001958.seq
|
ccc98dede3c807349b8a017ab8f200cb
|
A001959
|
u-pile numbers for the 3-Wythoff game with i=2.
|
[
"0",
"2",
"3",
"4",
"6",
"7",
"8",
"9",
"11",
"12",
"13",
"15",
"16",
"17",
"19",
"20",
"21",
"23",
"24",
"25",
"26",
"28",
"29",
"30",
"32",
"33",
"34",
"36",
"37",
"38",
"39",
"41",
"42",
"43",
"45",
"46",
"47",
"49",
"50",
"51",
"52",
"54",
"55",
"56",
"58",
"59",
"60",
"62",
"63",
"64",
"66",
"67",
"68",
"69",
"71",
"72",
"73",
"75",
"76",
"77",
"79",
"80",
"81",
"82",
"84",
"85",
"86",
"88"
] |
[
"nonn",
"easy"
] | 21 | 0 | 2 |
[
"A001954",
"A001958",
"A001959",
"A001960",
"A001963",
"A001968"
] |
[
"M0541"
] |
N. J. A. Sloane
| 2022-02-04T00:43:53 |
oeisdata/seq/A001/A001959.seq
|
cd63d9faabd389246bdce1e3d23b4f6d
|
A001960
|
a(n) = floor((n+2/3)*(5+sqrt(13))/2); v-pile positions in the 3-Wythoff game.
|
[
"2",
"7",
"11",
"15",
"20",
"24",
"28",
"32",
"37",
"41",
"45",
"50",
"54",
"58",
"63",
"67",
"71",
"76",
"80",
"84",
"88",
"93",
"97",
"101",
"106",
"110",
"114",
"119",
"123",
"127",
"131",
"136",
"140",
"144",
"149",
"153",
"157",
"162",
"166",
"170",
"174",
"179",
"183",
"187",
"192",
"196",
"200",
"205",
"209",
"213",
"218",
"222",
"226",
"230",
"235",
"239",
"243",
"248"
] |
[
"nonn"
] | 39 | 0 | 1 |
[
"A001954",
"A001957",
"A001958",
"A001959",
"A001960",
"A001963",
"A001968"
] |
[
"M1735",
"N0687"
] |
N. J. A. Sloane
| 2021-12-27T10:47:41 |
oeisdata/seq/A001/A001960.seq
|
c12ddd810c6113aaafbf684b84c0e9b1
|
A001961
|
A Beatty sequence: floor(n * (sqrt(5) - 1)).
|
[
"1",
"2",
"3",
"4",
"6",
"7",
"8",
"9",
"11",
"12",
"13",
"14",
"16",
"17",
"18",
"19",
"21",
"22",
"23",
"24",
"25",
"27",
"28",
"29",
"30",
"32",
"33",
"34",
"35",
"37",
"38",
"39",
"40",
"42",
"43",
"44",
"45",
"46",
"48",
"49",
"50",
"51",
"53",
"54",
"55",
"56",
"58",
"59",
"60",
"61",
"63",
"64",
"65",
"66",
"67",
"69",
"70",
"71",
"72",
"74",
"75",
"76",
"77",
"79",
"80",
"81",
"82",
"84"
] |
[
"nonn",
"easy"
] | 49 | 1 | 2 |
[
"A001961",
"A001962",
"A001965",
"A005206"
] |
[
"M0540",
"N0192"
] |
N. J. A. Sloane
| 2022-08-11T03:36:05 |
oeisdata/seq/A001/A001961.seq
|
4be350d02a890e69bb87e39004d5a398
|
A001962
|
A Beatty sequence: floor(n * (sqrt(5) + 3)).
|
[
"5",
"10",
"15",
"20",
"26",
"31",
"36",
"41",
"47",
"52",
"57",
"62",
"68",
"73",
"78",
"83",
"89",
"94",
"99",
"104",
"109",
"115",
"120",
"125",
"130",
"136",
"141",
"146",
"151",
"157",
"162",
"167",
"172",
"178",
"183",
"188",
"193",
"198",
"204",
"209",
"214",
"219",
"225",
"230",
"235",
"240",
"246",
"251",
"256",
"261",
"267",
"272",
"277",
"282",
"287"
] |
[
"nonn"
] | 54 | 1 | 1 |
[
"A001950",
"A001961",
"A001962"
] |
[
"M3795",
"N1548"
] |
N. J. A. Sloane
| 2021-04-29T21:24:15 |
oeisdata/seq/A001/A001962.seq
|
8d4468028c51f622d94266dc27393876
|
A001963
|
Winning positions in the u-pile of the 4-Wythoff game with i=1.
|
[
"0",
"1",
"2",
"4",
"5",
"6",
"7",
"8",
"10",
"11",
"12",
"13",
"15",
"16",
"17",
"18",
"20",
"21",
"22",
"23",
"25",
"26",
"27",
"28",
"29",
"31",
"32",
"33",
"34",
"36",
"37",
"38",
"39",
"41",
"42",
"43",
"44",
"46",
"47",
"48",
"49",
"50",
"52",
"53",
"54",
"55",
"57",
"58",
"59",
"60",
"62",
"63",
"64",
"65",
"67",
"68",
"69",
"70",
"72",
"73",
"74",
"75",
"76",
"78",
"79",
"80",
"81",
"83"
] |
[
"nonn",
"easy"
] | 31 | 0 | 3 |
[
"A001954",
"A001958",
"A001959",
"A001963",
"A001964",
"A001968"
] |
[
"M0943",
"N0354"
] |
N. J. A. Sloane
| 2022-02-04T00:43:29 |
oeisdata/seq/A001/A001963.seq
|
b65f270e9293388fc1da8abd389886d2
|
A001964
|
v-pile positions of the 4-Wythoff game with i=1.
|
[
"1",
"6",
"11",
"17",
"22",
"27",
"32",
"37",
"43",
"48",
"53",
"58",
"64",
"69",
"74",
"79",
"85",
"90",
"95",
"100",
"106",
"111",
"116",
"121",
"126",
"132",
"137",
"142",
"147",
"153",
"158",
"163",
"168",
"174",
"179",
"184",
"189",
"195",
"200",
"205",
"210",
"215",
"221",
"226",
"231",
"236",
"242",
"247",
"252",
"257",
"263",
"268",
"273",
"278",
"284",
"289"
] |
[
"nonn",
"easy"
] | 31 | 0 | 2 |
[
"A001963",
"A001964"
] |
[
"M4086",
"N1695"
] |
N. J. A. Sloane
| 2022-02-04T00:43:20 |
oeisdata/seq/A001/A001964.seq
|
061182e6c6c2df17c6a447b8661c8e50
|
A001965
|
u-pile count for the 4-Wythoff game with i=2.
|
[
"0",
"1",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"11",
"12",
"14",
"15",
"16",
"17",
"19",
"20",
"21",
"22",
"24",
"25",
"26",
"27",
"29",
"30",
"31",
"32",
"33",
"35",
"36",
"37",
"38",
"40",
"41",
"42",
"43",
"45",
"46",
"47",
"48",
"50",
"51",
"52",
"53",
"55",
"56",
"57",
"58",
"59",
"61",
"62",
"63",
"64",
"66",
"67",
"68",
"69",
"71",
"72",
"73",
"74",
"76",
"77",
"78",
"79",
"80",
"82"
] |
[
"nonn",
"easy"
] | 42 | 0 | 3 |
[
"A001961",
"A001965",
"A001966",
"A005206"
] |
[
"M2301",
"N0907"
] |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001965.seq
|
8df9cb0b9713a1ce647e8566871ccc42
|
A001966
|
v-pile counts for the 4-Wythoff game with i=2.
|
[
"2",
"7",
"13",
"18",
"23",
"28",
"34",
"39",
"44",
"49",
"54",
"60",
"65",
"70",
"75",
"81",
"86",
"91",
"96",
"102",
"107",
"112",
"117",
"123",
"128",
"133",
"138",
"143",
"149",
"154",
"159",
"164",
"170",
"175",
"180",
"185",
"191",
"196",
"201",
"206",
"212",
"217",
"222",
"227",
"233",
"238",
"243",
"248",
"253",
"259",
"264",
"269",
"274",
"280",
"285",
"290"
] |
[
"nonn",
"easy"
] | 34 | 0 | 1 |
[
"A001950",
"A001965",
"A001966"
] |
[
"M1739",
"N0689"
] |
N. J. A. Sloane
| 2022-08-26T05:35:49 |
oeisdata/seq/A001/A001966.seq
|
cde636a6e74578a491e2e7745625808f
|
A001967
|
u-pile positions for the 4-Wythoff game with i=3.
|
[
"0",
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"10",
"12",
"13",
"14",
"15",
"16",
"18",
"19",
"20",
"21",
"23",
"24",
"25",
"26",
"28",
"29",
"30",
"31",
"33",
"34",
"35",
"36",
"38",
"39",
"40",
"41",
"42",
"44",
"45",
"46",
"47",
"49",
"50",
"51",
"52",
"54",
"55",
"56",
"57",
"59",
"60",
"61",
"62",
"63",
"65",
"66",
"67",
"68",
"70",
"71",
"72",
"73",
"75",
"76",
"77",
"78",
"80",
"81",
"82",
"83"
] |
[
"nonn",
"easy"
] | 26 | 0 | 2 |
[
"A001967",
"A001968"
] |
[
"M0515",
"N0184"
] |
N. J. A. Sloane
| 2022-02-04T08:15:00 |
oeisdata/seq/A001/A001967.seq
|
96074347923a85b377b442ba6d19943b
|
A001968
|
v-pile positions of the 4-Wythoff game with i=3.
|
[
"3",
"9",
"14",
"19",
"24",
"30",
"35",
"40",
"45",
"51",
"56",
"61",
"66",
"71",
"77",
"82",
"87",
"92",
"98",
"103",
"108",
"113",
"119",
"124",
"129",
"134",
"140",
"145",
"150",
"155",
"161",
"166",
"171",
"176",
"181",
"187",
"192",
"197",
"202",
"208",
"213",
"218",
"223",
"229",
"234",
"239",
"244",
"250",
"255",
"260",
"265",
"270",
"276",
"281",
"286",
"291"
] |
[
"nonn",
"easy"
] | 21 | 0 | 1 |
[
"A001967",
"A001968"
] |
[
"M2769",
"N1113"
] |
N. J. A. Sloane
| 2022-02-04T00:42:13 |
oeisdata/seq/A001/A001968.seq
|
6826b3888642b1e158cbf8c104bb0503
|
A001969
|
Evil numbers: nonnegative integers with an even number of 1's in their binary expansion.
|
[
"0",
"3",
"5",
"6",
"9",
"10",
"12",
"15",
"17",
"18",
"20",
"23",
"24",
"27",
"29",
"30",
"33",
"34",
"36",
"39",
"40",
"43",
"45",
"46",
"48",
"51",
"53",
"54",
"57",
"58",
"60",
"63",
"65",
"66",
"68",
"71",
"72",
"75",
"77",
"78",
"80",
"83",
"85",
"86",
"89",
"90",
"92",
"95",
"96",
"99",
"101",
"102",
"105",
"106",
"108",
"111",
"113",
"114",
"116",
"119",
"120",
"123",
"125",
"126",
"129"
] |
[
"easy",
"core",
"nonn",
"nice",
"base"
] | 255 | 1 | 2 |
[
"A000069",
"A000120",
"A000788",
"A001969",
"A006068",
"A006364",
"A010060",
"A018900",
"A023416",
"A027699",
"A036585",
"A048724",
"A059010",
"A059015",
"A094677",
"A130593",
"A133009"
] |
[
"M2395",
"N0952"
] |
N. J. A. Sloane
| 2025-03-18T10:33:05 |
oeisdata/seq/A001/A001969.seq
|
6051f7d4d808389c14281c07c73b5ad9
|
A001970
|
Functional determinants; partitions of partitions; Euler transform applied twice to all 1's sequence.
|
[
"1",
"1",
"3",
"6",
"14",
"27",
"58",
"111",
"223",
"424",
"817",
"1527",
"2870",
"5279",
"9710",
"17622",
"31877",
"57100",
"101887",
"180406",
"318106",
"557453",
"972796",
"1688797",
"2920123",
"5026410",
"8619551",
"14722230",
"25057499",
"42494975",
"71832114",
"121024876",
"203286806",
"340435588",
"568496753",
"946695386"
] |
[
"nonn",
"nice",
"easy"
] | 137 | 0 | 3 |
[
"A000041",
"A000219",
"A001055",
"A001383",
"A001970",
"A006171",
"A050336",
"A055885",
"A055887",
"A061255",
"A061256",
"A061257",
"A061259",
"A061260",
"A063834",
"A072233",
"A089292",
"A089300",
"A112798",
"A271619",
"A275024",
"A290353",
"A316980"
] |
[
"M2576",
"N1019"
] |
N. J. A. Sloane
| 2025-06-16T23:49:55 |
oeisdata/seq/A001/A001970.seq
|
f7b6c2ec094489ce245a5b201d306caf
|
A001971
|
Nearest integer to n^2/8.
|
[
"0",
"0",
"1",
"1",
"2",
"3",
"5",
"6",
"8",
"10",
"13",
"15",
"18",
"21",
"25",
"28",
"32",
"36",
"41",
"45",
"50",
"55",
"61",
"66",
"72",
"78",
"85",
"91",
"98",
"105",
"113",
"120",
"128",
"136",
"145",
"153",
"162",
"171",
"181",
"190",
"200",
"210",
"221",
"231",
"242",
"253",
"265",
"276",
"288",
"300",
"313",
"325",
"338",
"351",
"365",
"378",
"392",
"406",
"421",
"435",
"450"
] |
[
"nonn",
"easy"
] | 123 | 0 | 5 |
[
"A000217",
"A000982",
"A001400",
"A001971",
"A026810",
"A061857",
"A261491"
] |
[
"M0625",
"N0227"
] |
N. J. A. Sloane
| 2023-07-02T02:21:00 |
oeisdata/seq/A001/A001971.seq
|
3ce40a471160cee3c46c4e07139635fb
|
A001972
|
Expansion of 1/((1-x)^2*(1-x^4)) = 1/( (1+x)*(1+x^2)*(1-x)^3 ).
|
[
"1",
"2",
"3",
"4",
"6",
"8",
"10",
"12",
"15",
"18",
"21",
"24",
"28",
"32",
"36",
"40",
"45",
"50",
"55",
"60",
"66",
"72",
"78",
"84",
"91",
"98",
"105",
"112",
"120",
"128",
"136",
"144",
"153",
"162",
"171",
"180",
"190",
"200",
"210",
"220",
"231",
"242",
"253",
"264",
"276",
"288",
"300",
"312",
"325",
"338",
"351",
"364",
"378",
"392",
"406",
"420",
"435",
"450",
"465"
] |
[
"nonn",
"easy"
] | 86 | 0 | 2 |
[
"A000217",
"A001972",
"A002620",
"A007590",
"A008621",
"A056594",
"A130519",
"A333260"
] |
[
"M0551",
"N0199"
] |
N. J. A. Sloane
| 2024-01-18T01:24:15 |
oeisdata/seq/A001/A001972.seq
|
c8dedc3c06daca40535b9db355fe2149
|
A001973
|
Expansion of (1+x^3)/((1-x)*(1-x^2)^2*(1-x^3)).
|
[
"1",
"1",
"3",
"5",
"8",
"12",
"18",
"24",
"33",
"43",
"55",
"69",
"86",
"104",
"126",
"150",
"177",
"207",
"241",
"277",
"318",
"362",
"410",
"462",
"519",
"579",
"645",
"715",
"790",
"870",
"956",
"1046",
"1143",
"1245",
"1353",
"1467",
"1588",
"1714",
"1848",
"1988"
] |
[
"nonn",
"easy"
] | 56 | 0 | 3 | null |
[
"M2441",
"N0969"
] |
N. J. A. Sloane
| 2023-03-30T14:19:23 |
oeisdata/seq/A001/A001973.seq
|
74ae97394101da5716aac9a07cde7417
|
A001974
|
Numbers that are the sum of 3 distinct squares, i.e., numbers of the form x^2 + y^2 + z^2 with 0 <= x < y < z.
|
[
"5",
"10",
"13",
"14",
"17",
"20",
"21",
"25",
"26",
"29",
"30",
"34",
"35",
"37",
"38",
"40",
"41",
"42",
"45",
"46",
"49",
"50",
"52",
"53",
"54",
"56",
"58",
"59",
"61",
"62",
"65",
"66",
"68",
"69",
"70",
"73",
"74",
"75",
"77",
"78",
"80",
"81",
"82",
"83",
"84",
"85",
"86",
"89",
"90",
"91",
"93",
"94",
"97",
"98",
"100",
"101",
"104",
"105",
"106",
"107",
"109",
"110",
"113"
] |
[
"nonn",
"easy",
"nice"
] | 41 | 1 | 1 |
[
"A001974",
"A001983",
"A004432",
"A004436",
"A024803",
"A025339",
"A025442"
] | null |
N. J. A. Sloane
| 2021-05-10T21:08:21 |
oeisdata/seq/A001/A001974.seq
|
655d0afc26ef5b0b6c28e9ebef122dea
|
A001975
|
Number of partitions of floor(5n/2) into n nonnegative integers each no more than 5.
|
[
"1",
"1",
"3",
"6",
"12",
"20",
"32",
"49",
"73",
"102",
"141",
"190",
"252",
"325",
"414",
"521",
"649",
"795",
"967",
"1165",
"1394",
"1651",
"1944",
"2275",
"2649",
"3061",
"3523",
"4035",
"4604",
"5225",
"5910",
"6660",
"7483",
"8372",
"9343",
"10395",
"11538",
"12764",
"14090",
"15516",
"17053",
"18691",
"20451",
"22330",
"24342",
"26476",
"28754"
] |
[
"nonn",
"easy"
] | 36 | 0 | 3 | null |
[
"M2551",
"N1010"
] |
N. J. A. Sloane
| 2022-02-04T00:41:57 |
oeisdata/seq/A001/A001975.seq
|
63b756be44c05548f4181f204f4c7770
|
A001976
|
Number of partitions of floor(5n/2)-1 into n nonnegative integers each no more than 5.
|
[
"0",
"1",
"3",
"6",
"11",
"19",
"32",
"48",
"71",
"101",
"141",
"188",
"249",
"322",
"414",
"518",
"645",
"791",
"966",
"1160",
"1389",
"1645",
"1943",
"2268",
"2642",
"3053",
"3521",
"4026",
"4596",
"5214",
"5907",
"6648",
"7473",
"8359",
"9339",
"10380",
"11526",
"12747",
"14085",
"15498",
"17039",
"18671",
"20444",
"22308",
"24326",
"26452",
"28746"
] |
[
"nonn",
"easy"
] | 26 | 0 | 3 |
[
"A001975",
"A001976"
] |
[
"M2545",
"N1006"
] |
N. J. A. Sloane
| 2023-06-25T02:48:39 |
oeisdata/seq/A001/A001976.seq
|
caae33d2ca6ef13e83e06ef6f4c08ad5
|
A001977
|
Number of partitions of 3n into n parts from the set {0, 1, ..., 6} (repetitions admissible).
|
[
"1",
"1",
"4",
"8",
"18",
"32",
"58",
"94",
"151",
"227",
"338",
"480",
"676",
"920",
"1242",
"1636",
"2137",
"2739",
"3486",
"4370",
"5444",
"6698",
"8196",
"9926",
"11963",
"14293",
"17002",
"20076",
"23612",
"27594",
"32134",
"37212",
"42955",
"49341",
"56512",
"64444",
"73294",
"83036",
"93844",
"105690",
"118765",
"133037"
] |
[
"nonn",
"easy"
] | 43 | 0 | 3 | null |
[
"M3335",
"N1342"
] |
N. J. A. Sloane
| 2022-02-04T08:15:09 |
oeisdata/seq/A001/A001977.seq
|
dbb7c2187b67a9817a7d3a97d18abda3
|
A001978
|
Number of partitions of 3n-1 into n nonnegative integers each no more than 6.
|
[
"0",
"1",
"3",
"8",
"16",
"32",
"55",
"94",
"147",
"227",
"332",
"480",
"668",
"920",
"1232",
"1635",
"2124",
"2738",
"3470",
"4368",
"5424",
"6695",
"8172",
"9922",
"11934",
"14287",
"16968",
"20068",
"23572",
"27584",
"32087",
"37199",
"42901",
"49325",
"56450",
"64424",
"73223",
"83012",
"93764",
"105661",
"118674",
"133003",
"148616"
] |
[
"nonn",
"easy"
] | 28 | 0 | 3 |
[
"A001977",
"A001978"
] |
[
"M2725",
"N1092"
] |
N. J. A. Sloane
| 2023-06-25T02:50:30 |
oeisdata/seq/A001/A001978.seq
|
775adc1ae6dade27f51d72d56ace1c7b
|
A001979
|
Number of partitions of floor(7n/2) into n nonnegative integers each no more than 7.
|
[
"1",
"1",
"4",
"10",
"24",
"49",
"94",
"169",
"289",
"468",
"734",
"1117",
"1656",
"2385",
"3370",
"4672",
"6375",
"8550",
"11322",
"14800",
"19138",
"24460",
"30982",
"38882",
"48417",
"59779",
"73316",
"89291",
"108108",
"130053",
"155646",
"185258",
"219489",
"258735",
"303748",
"355034",
"413442",
"479500",
"554256"
] |
[
"nonn",
"easy"
] | 36 | 0 | 3 |
[
"A001979",
"A001980"
] |
[
"M3389",
"N1369"
] |
N. J. A. Sloane
| 2023-06-25T02:52:17 |
oeisdata/seq/A001/A001979.seq
|
af76a4ad930e1e381aad5fc40cb9377d
|
A001980
|
Number of partitions of floor(7n/2)-1 into n nonnegative integers each no greater than 7.
|
[
"0",
"1",
"4",
"10",
"23",
"48",
"94",
"166",
"285",
"464",
"734",
"1109",
"1646",
"2371",
"3366",
"4652",
"6357",
"8519",
"11309",
"14754",
"19103",
"24399",
"30956",
"38797",
"48355",
"59665",
"73264",
"89145",
"108011",
"129864",
"155554",
"185017",
"219336",
"258438",
"303604",
"354665",
"413213",
"479048",
"554033"
] |
[
"nonn",
"easy"
] | 35 | 0 | 3 |
[
"A001979",
"A001980"
] |
[
"M3388",
"N1368"
] |
N. J. A. Sloane
| 2023-10-27T21:08:49 |
oeisdata/seq/A001/A001980.seq
|
4488d2bb61ae8f124633a8f396a00316
|
A001981
|
Restricted partitions.
|
[
"1",
"1",
"5",
"13",
"33",
"73",
"151",
"289",
"526",
"910",
"1514",
"2430",
"3788",
"5744",
"8512",
"12346",
"17575",
"24591",
"33885",
"46029",
"61731",
"81805",
"107233",
"139143",
"178870",
"227930",
"288100",
"361384",
"450096",
"556834",
"684572",
"836618",
"1016737",
"1229093",
"1478379",
"1769773"
] |
[
"nonn"
] | 35 | 0 | 3 | null |
[
"M3832",
"N1572"
] |
N. J. A. Sloane
| 2019-01-25T03:25:32 |
oeisdata/seq/A001/A001981.seq
|
86cbe93e4e7f049add69dd155f9ccbe1
|
A001982
|
Number of partitions of 4n-1 into n nonnegative integers each no greater than 8.
|
[
"0",
"1",
"4",
"12",
"31",
"71",
"147",
"285",
"519",
"902",
"1502",
"2417",
"3768",
"5722",
"8481",
"12310",
"17528",
"24537",
"33814",
"45949",
"61629",
"81688",
"107089",
"138979",
"178669",
"227703",
"287828",
"361075",
"449731",
"556423",
"684089",
"836078",
"1016110",
"1228391",
"1477573",
"1768875",
"2108041",
"2501480"
] |
[
"nonn",
"easy"
] | 26 | 0 | 3 |
[
"A001981",
"A001982"
] |
[
"M3441",
"N1396"
] |
N. J. A. Sloane
| 2023-06-25T02:54:50 |
oeisdata/seq/A001/A001982.seq
|
c9a00eb73aa329c492ac83b9c9d037bf
|
A001983
|
Numbers that are the sum of 2 distinct squares: of form x^2 + y^2 with 0 <= x < y.
|
[
"1",
"4",
"5",
"9",
"10",
"13",
"16",
"17",
"20",
"25",
"26",
"29",
"34",
"36",
"37",
"40",
"41",
"45",
"49",
"50",
"52",
"53",
"58",
"61",
"64",
"65",
"68",
"73",
"74",
"80",
"81",
"82",
"85",
"89",
"90",
"97",
"100",
"101",
"104",
"106",
"109",
"113",
"116",
"117",
"121",
"122",
"125",
"130",
"136",
"137",
"144",
"145",
"146",
"148",
"149",
"153",
"157",
"160",
"164"
] |
[
"nonn",
"easy",
"nice"
] | 52 | 1 | 2 |
[
"A000290",
"A000404",
"A001481",
"A001983",
"A004431",
"A004435",
"A025435"
] | null |
N. J. A. Sloane
| 2023-01-02T09:02:24 |
oeisdata/seq/A001/A001983.seq
|
7512322c14f81c5a16ccffadaf940d5d
|
A001984
|
Erroneous version of A045535.
|
[
"7",
"23",
"71",
"311",
"479",
"1559",
"5711",
"10559",
"18191",
"31391",
"307271",
"366791",
"366791",
"2155919"
] |
[
"dead"
] | 9 | 1 | 1 | null | null | null | 2015-07-25T20:00:57 |
oeisdata/seq/A001/A001984.seq
|
2933f61190faaebeaaff7c5862695515
|
A001985
|
Class numbers of quadratic fields.
|
[
"3",
"7",
"19",
"25",
"51",
"109",
"153",
"213",
"289",
"1121",
"1121",
"1121",
"3997",
"7457",
"12017",
"12719",
"20299",
"24503",
"24503",
"25817",
"25817",
"128755",
"128755",
"219207",
"456929",
"456929",
"761619",
"883537"
] |
[
"nonn",
"more"
] | 17 | 3 | 1 | null |
[
"M2669",
"N1068"
] |
N. J. A. Sloane
| 2022-02-04T00:39:48 |
oeisdata/seq/A001/A001985.seq
|
6078c93a8a5de35460c566dd025b5bf7
|
A001986
|
Let p be the n-th odd prime. Then a(n) is the least prime congruent to 3 modulo 8 such that Legendre(-a(n), q) = -1 for all odd primes q <= p.
|
[
"19",
"43",
"43",
"67",
"67",
"163",
"163",
"163",
"163",
"163",
"163",
"222643",
"1333963",
"1333963",
"2404147",
"2404147",
"20950603",
"51599563",
"51599563",
"96295483",
"96295483",
"146161723",
"1408126003",
"3341091163",
"3341091163",
"3341091163",
"52947440683",
"52947440683",
"52947440683",
"193310265163"
] |
[
"nonn"
] | 45 | 1 | 1 |
[
"A001986",
"A001987",
"A001992",
"A094841",
"A094842",
"A094843",
"A094844",
"A094845",
"A094846",
"A094851",
"A094852",
"A094853"
] |
[
"M5073",
"N2195"
] |
N. J. A. Sloane
| 2020-04-10T11:36:09 |
oeisdata/seq/A001/A001986.seq
|
09ad409d15f3931a464f393e8afd4010
|
A001987
|
Class numbers associated with terms of A001986.
|
[
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"33",
"79",
"79",
"107",
"107",
"311",
"487",
"487",
"665",
"665",
"857",
"2293",
"3523",
"3523",
"3523",
"13909",
"13909",
"13909",
"26713",
"29351",
"29351",
"59801",
"70877",
"70877",
"70877",
"70877",
"296475",
"296475",
"296475",
"296475",
"3201195"
] |
[
"nonn"
] | 27 | 1 | 12 |
[
"A001986",
"A001987",
"A094842",
"A094846",
"A094851"
] |
[
"M5235",
"N2278"
] |
N. J. A. Sloane
| 2023-11-04T13:44:03 |
oeisdata/seq/A001/A001987.seq
|
59ce053ef91146a1e143acbffdafd0fd
|
A001988
|
Let p be the n-th odd prime. a(n) is the least prime congruent to 7 modulo 8 such that Legendre(-a(n), q) = -Legendre(-1, q) for all odd primes q <= p.
|
[
"7",
"7",
"127",
"463",
"463",
"487",
"1423",
"33247",
"73327",
"118903",
"118903",
"118903",
"454183",
"773767",
"773767",
"773767",
"773767",
"86976583",
"125325127",
"132690343",
"788667223",
"788667223",
"1280222287",
"2430076903",
"10703135983",
"10703135983",
"10703135983"
] |
[
"nonn"
] | 35 | 1 | 1 |
[
"A001988",
"A001990"
] |
[
"M4333",
"N1888"
] |
N. J. A. Sloane
| 2022-02-04T02:01:57 |
oeisdata/seq/A001/A001988.seq
|
ac450ebc32a7b2b9866d207c99b90afb
|
A001989
|
Class numbers associated with terms of A001988.
|
[
"1",
"1",
"5",
"7",
"7",
"7",
"9",
"53",
"73",
"83",
"83",
"83",
"157",
"185",
"185",
"185",
"185",
"1927",
"2295",
"2273",
"5313",
"5313",
"7173",
"9529",
"18545",
"18545",
"18545",
"18545",
"22635",
"22635",
"66011",
"121725",
"344909",
"344909"
] |
[
"nonn"
] | 28 | 1 | 3 |
[
"A001988",
"A001989"
] |
[
"M3756",
"N1535"
] |
N. J. A. Sloane
| 2022-11-19T04:39:02 |
oeisdata/seq/A001/A001989.seq
|
629c285b3e43ec35e01ba16d228d8493
|
A001990
|
Let p be the n-th odd prime. a(n) is the least prime congruent to 5 modulo 8 such that Legendre(-a(n), q) = -Legendre(-2, q) for all odd primes q <= p.
|
[
"5",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"23669",
"23669",
"23669",
"23669",
"23669",
"23669",
"1508789",
"5025869",
"9636461",
"9636461",
"9636461",
"37989701",
"37989701",
"37989701",
"37989701",
"37989701",
"240511301",
"240511301"
] |
[
"nonn"
] | 27 | 1 | 1 |
[
"A001988",
"A001990"
] |
[
"M3953",
"N1632"
] |
N. J. A. Sloane
| 2022-02-04T02:01:53 |
oeisdata/seq/A001/A001990.seq
|
32a06d332be7e6df1727680278795a67
|
A001991
|
Class numbers associated with terms of A001990.
|
[
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"46",
"46",
"46",
"46",
"46",
"46",
"406",
"718",
"950",
"950",
"950",
"1698",
"1698",
"1698",
"1698",
"1698",
"3990",
"3990",
"3990",
"53510",
"77970",
"89478",
"89478",
"89478",
"89478",
"89478",
"89478"
] |
[
"nonn",
"more"
] | 31 | 1 | 1 |
[
"A001990",
"A001991"
] |
[
"M0212",
"N0863"
] |
N. J. A. Sloane
| 2022-11-19T04:39:13 |
oeisdata/seq/A001/A001991.seq
|
485e408dc8afbb8fc0599576a47faf8a
|
A001992
|
Let p = n-th odd prime. Then a(n) = least prime congruent to 5 modulo 8 such that Legendre(a(n), q) = -1 for all odd primes q <= p.
|
[
"5",
"53",
"173",
"173",
"293",
"2477",
"9173",
"9173",
"61613",
"74093",
"74093",
"74093",
"170957",
"360293",
"679733",
"2004917",
"2004917",
"69009533",
"138473837",
"237536213",
"384479933",
"883597853",
"1728061733",
"1728061733",
"1728061733",
"1728061733"
] |
[
"nonn"
] | 33 | 1 | 1 |
[
"A001986",
"A001987",
"A001992",
"A094845",
"A094846",
"A094847",
"A094848",
"A094849",
"A094850",
"A094851",
"A094852",
"A094853"
] |
[
"M4012",
"N1663"
] |
N. J. A. Sloane
| 2019-02-21T15:07:42 |
oeisdata/seq/A001/A001992.seq
|
98845954951f7c3fc53ec9d28e9b2a9b
|
A001993
|
Number of two-rowed partitions of length 3.
|
[
"1",
"1",
"3",
"5",
"9",
"13",
"22",
"30",
"45",
"61",
"85",
"111",
"150",
"190",
"247",
"309",
"390",
"478",
"593",
"715",
"870",
"1038",
"1243",
"1465",
"1735",
"2023",
"2368",
"2740",
"3175",
"3643",
"4189",
"4771",
"5443",
"6163",
"6982",
"7858",
"8852",
"9908",
"11098",
"12366",
"13780",
"15284",
"16958",
"18730",
"20692",
"22772",
"25058",
"27478"
] |
[
"nonn",
"easy"
] | 33 | 0 | 3 | null |
[
"M2452",
"N0973"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A001/A001993.seq
|
d9f7bac7b98f558021a286d0eceb04e9
|
A001994
|
Expansion of 1/((1-x^2)*(1-x^4)^2*(1-x^6)*(1-x^8)*(1-x^10)) (even powers only).
|
[
"1",
"1",
"3",
"4",
"8",
"11",
"18",
"24",
"36",
"47",
"66",
"84",
"113",
"141",
"183",
"225",
"284",
"344",
"425",
"508",
"617",
"729",
"872",
"1020",
"1205",
"1397",
"1632",
"1877",
"2172",
"2480",
"2846",
"3228",
"3677",
"4146",
"4691",
"5261",
"5917",
"6603",
"7386",
"8205",
"9133",
"10103",
"11195",
"12336",
"13613",
"14947",
"16431",
"17981",
"19697"
] |
[
"nonn",
"easy"
] | 27 | 0 | 3 |
[
"A001994",
"A001996"
] |
[
"M2348",
"N0927"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A001/A001994.seq
|
96e4d4f0044b3322bb36bf98fc8ae90d
|
A001995
|
Numbers that are the sum of 5 distinct squares: of form v^2 + w^2 + x^2 + y^2 + z^2 with 0 <= v < w < x < y < z.
|
[
"30",
"39",
"46",
"50",
"51",
"54",
"55",
"57",
"62",
"63",
"65",
"66",
"70",
"71",
"74",
"75",
"78",
"79",
"81",
"82",
"84",
"85",
"86",
"87",
"88",
"90",
"91",
"93",
"94",
"95",
"98",
"99",
"100",
"102",
"103",
"105",
"106",
"107",
"109",
"110",
"111",
"113",
"114",
"115",
"116",
"117",
"118",
"119",
"120",
"121",
"122",
"123",
"125",
"126",
"127",
"129",
"130",
"131"
] |
[
"nonn"
] | 15 | 1 | 1 |
[
"A001944",
"A001995"
] | null |
N. J. A. Sloane
| 2022-02-04T00:38:11 |
oeisdata/seq/A001/A001995.seq
|
8bee66230449f950a985c70946e725a8
|
A001996
|
Number of partitions of n into parts 2, 3, 4, 5, 6, 7.
|
[
"1",
"0",
"1",
"1",
"2",
"2",
"4",
"4",
"6",
"7",
"10",
"11",
"16",
"17",
"23",
"26",
"33",
"37",
"47",
"52",
"64",
"72",
"86",
"96",
"115",
"127",
"149",
"166",
"192",
"212",
"245",
"269",
"307",
"338",
"382",
"419",
"472",
"515",
"576",
"629",
"699",
"760",
"843",
"913",
"1007",
"1091",
"1197",
"1293",
"1416",
"1525",
"1663",
"1790",
"1945",
"2088",
"2265",
"2426"
] |
[
"nonn",
"easy"
] | 29 | 0 | 5 |
[
"A001996",
"A008667",
"A037145",
"A059841",
"A103221",
"A266755",
"A266776",
"A266781"
] |
[
"M0306",
"N0112"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A001/A001996.seq
|
007b7ec90ac9afcb9e28562185fa979d
|
A001997
|
Number of different shapes formed by bending a piece of wire of length n in the plane.
|
[
"1",
"1",
"2",
"4",
"10",
"24",
"66",
"176",
"493",
"1362",
"3821",
"10660",
"29864",
"83329",
"232702",
"648182",
"1804901",
"5015725",
"13931755",
"38635673",
"107090666",
"296449133",
"820271143",
"2267225157",
"6264244414",
"17291930470"
] |
[
"nonn",
"more",
"nice",
"walk",
"changed"
] | 39 | 0 | 3 |
[
"A001997",
"A001998",
"A006817"
] |
[
"M1206",
"N0465"
] |
N. J. A. Sloane
| 2025-07-08T16:27:20 |
oeisdata/seq/A001/A001997.seq
|
9445dcef0e727016a179e85e574e64ab
|
A001998
|
Bending a piece of wire of length n+1; walks of length n+1 on a tetrahedron; also non-branched catafusenes with n+2 condensed hexagons.
|
[
"1",
"2",
"4",
"10",
"25",
"70",
"196",
"574",
"1681",
"5002",
"14884",
"44530",
"133225",
"399310",
"1196836",
"3589414",
"10764961",
"32291602",
"96864964",
"290585050",
"871725625",
"2615147350",
"7845353476",
"23535971854",
"70607649841",
"211822683802",
"635467254244",
"1906400965570",
"5719200505225",
"17157599124190"
] |
[
"nonn",
"nice",
"easy"
] | 162 | 0 | 2 |
[
"A000228",
"A001444",
"A001997",
"A001998",
"A002216",
"A005418",
"A005963",
"A007051",
"A036359",
"A038766",
"A056323",
"A056324",
"A056325",
"A103293",
"A107767",
"A124302",
"A182522",
"A320750",
"A323942",
"A345207"
] |
[
"M1211",
"N0468"
] |
N. J. A. Sloane
| 2024-05-21T08:46:52 |
oeisdata/seq/A001/A001998.seq
|
9c0e25c51f218c5885304bb97fa2f7e9
|
A001999
|
a(n) = a(n-1)*(a(n-1)^2 - 3).
|
[
"3",
"18",
"5778",
"192900153618",
"7177905237579946589743592924684178"
] |
[
"nonn",
"easy",
"nice"
] | 66 | 0 | 1 |
[
"A000032",
"A001566",
"A001999",
"A002814",
"A006276",
"A045529",
"A112845",
"A219160",
"A219161",
"A219162"
] |
[
"M3055",
"N1239"
] |
N. J. A. Sloane
| 2025-02-16T08:32:24 |
oeisdata/seq/A001/A001999.seq
|
722d43a508d48727a9aaa769b922da8d
|
A002000
|
a(n+1) = a(n)*(a(n)^2 - 3) with a(0) = 7.
|
[
"7",
"322",
"33385282",
"37210469265847998489922",
"51522323599677629496737990329528638956583548304378053615581043535682"
] |
[
"nonn",
"easy"
] | 38 | 0 | 1 |
[
"A000032",
"A001999",
"A002000",
"A006267",
"A219161",
"A271223"
] |
[
"M4463",
"N1892"
] |
N. J. A. Sloane
| 2022-11-19T20:36:45 |
oeisdata/seq/A002/A002000.seq
|
800ebcd5634a8a9f37599967e6c68e10
|
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