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christopher
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oeis

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1999-12-11 03:00:00
2025-04-25 01:21:50
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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
5
[ "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
5
[ "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" ]
67
0
5
[ "A000420", "A001148", "A001903", "A010879", "A131707", "A159966" ]
null
N. J. A. Sloane
2023-12-14T06:16:56
oeisdata/seq/A001/A001903.seq
33c9de94384fe3b61b0daac9edcd51a1
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
5
[ "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
0
5
[ "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
5
[ "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
5
[ "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
5
[ "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", "changed" ]
55
0
5
[ "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
3477d5658cec6b3b98d22088d4719355
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
0
5
[ "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" ]
172
0
5
[ "A000032", "A000045", "A000071", "A001611", "A001911", "A006327", "A011794", "A101220", "A108617", "A157725", "A157726", "A157727", "A157728", "A157729", "A165910", "A167616", "A181631", "A226538", "A261019" ]
[ "M2546", "N1007" ]
N. J. A. Sloane
2024-10-30T19:29:31
oeisdata/seq/A001/A001911.seq
e11b4bb5bf3edf7a1a23b794f5b92e47
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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
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
5
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" ]
73
0
5
[ "A000217", "A001570", "A001652", "A001921", "A001922", "A006051", "A006451", "A129556", "A233450" ]
[ "M4455", "N1885" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001921.seq
726f405fbf323281576c7c53f9ab3bfd
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" ]
81
0
5
[ "A001075", "A001353", "A001570", "A001844", "A001921", "A001922", "A003215", "A005448", "A006051", "A016754", "A076139", "A156712" ]
[ "M4569", "N1946" ]
N. J. A. Sloane
2022-10-07T09:09:44
oeisdata/seq/A001/A001922.seq
1026c1d969efc67b64ac1a1d949bdaf9
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
5
[ "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" ]
188
0
5
[ "A000045", "A001891", "A001924", "A011794", "A014162", "A039834", "A065220", "A077880", "A122595", "A129696", "A133640", "A141289" ]
[ "M2645", "N1053" ]
N. J. A. Sloane
2025-01-06T10:57:53
oeisdata/seq/A001/A001924.seq
6342fc24e48324495cb8325d1bf1bd71
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
5
[ "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
5
[ "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" ]
52
0
5
[ "A000110", "A000112", "A000608", "A000798", "A001035", "A001927", "A001929", "A006056", "A006057", "A006058", "A006059", "A066303", "A342501" ]
[ "M2043", "N0809" ]
N. J. A. Sloane.
2021-03-14T11:41:27
oeisdata/seq/A001/A001927.seq
f697a9938f9d5bd9193fca5dd772ce72
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
5
[ "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
5
[ "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
5
[ "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
0
5
[ "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" ]
66
0
5
null
[ "M0844", "N0319" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001932.seq
f25ec9557cb59038eae31d148fa554d7
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
0
5
[ "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" ]
95
0
5
[ "A000122", "A000203", "A001934", "A002318", "A002513", "A004403", "A004404", "A004425", "A015128" ]
[ "M3443", "N1397" ]
N. J. A. Sloane, Simon Plouffe
2024-07-30T04:21:00
oeisdata/seq/A001/A001934.seq
fe1846574097d362011952cf2f360da7
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" ]
176
0
5
[ "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
2025-02-16T08:32:24
oeisdata/seq/A001/A001935.seq
09818cc104d39acb85e16c7e73d8b4bd
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
5
[ "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
5
[ "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
5
[ "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
5
[ "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
5
[ "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
5
[ "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
5
[ "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
5
[ "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
0
5
[ "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" ]
84
0
5
[ "A001351", "A001608", "A001945", "A078712", "A104499" ]
[ "M3730", "N1525" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001945.seq
5498ba9917b81e511156030d69518146
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
5
[ "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
5
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
0
5
[ "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
5
[ "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", "changed" ]
261
0
5
[ "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
53b4ad9e5f3c8f041d5331508c69f7d5
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" ]
165
0
5
[ "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
2025-02-16T08:32:24
oeisdata/seq/A001/A001951.seq
05a5959f162f5506ce24f5a99fc25d6c
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
0
5
[ "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
5
[ "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
5
[ "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
0
5
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
0
5
[ "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
5
[ "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
5
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
5
[ "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
5
[ "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
0
5
[ "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
0
5
[ "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
5
[ "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
5
[ "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
5
[ "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
5
[ "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
5
[ "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
5
[ "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
0
5
[ "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" ]
134
0
5
[ "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
2024-11-13T16:38:10
oeisdata/seq/A001/A001970.seq
be4b8f30281f603c6082447bfb3d7715
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
5
[ "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
5
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
0
5
[ "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
5
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
5
[ "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
5
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
5
[ "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
5
[ "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
5
[ "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
5
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
5
[ "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
0
5
[ "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
0
5
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
0
5
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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
[ "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
0
5
[ "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" ]
32
0
5
null
[ "M2452", "N0973" ]
N. J. A. Sloane
2023-06-25T02:56:07
oeisdata/seq/A001/A001993.seq
3028d649d941ce3eeb9fba43f806265d
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" ]
26
0
5
[ "A001994", "A001996" ]
[ "M2348", "N0927" ]
N. J. A. Sloane
2023-09-28T14:07:44
oeisdata/seq/A001/A001994.seq
f0a31c8f5727123a6d0c065c34b761ad
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
0
5
[ "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" ]
28
0
5
[ "A001996", "A008667", "A037145", "A059841", "A103221", "A266755", "A266776", "A266781" ]
[ "M0306", "N0112" ]
N. J. A. Sloane
2021-12-19T10:11:04
oeisdata/seq/A001/A001996.seq
7c9c2d0a571e75ec8ab24a936b811366
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" ]
35
0
5
[ "A001997", "A001998", "A006817" ]
[ "M1206", "N0465" ]
N. J. A. Sloane.
2025-02-16T08:32:24
oeisdata/seq/A001/A001997.seq
23c9d7f8a1ff2344a96009e68dc99be8
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
5
[ "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
5
[ "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
5
[ "A000032", "A001999", "A002000", "A006267", "A219161", "A271223" ]
[ "M4463", "N1892" ]
N. J. A. Sloane
2022-11-19T20:36:45
oeisdata/seq/A002/A002000.seq
800ebcd5634a8a9f37599967e6c68e10