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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A006001
Number of paraffins.
[ "1", "4", "10", "22", "43", "76", "124", "190", "277", "388", "526", "694", "895", "1132", "1408", "1726", "2089", "2500", "2962", "3478", "4051", "4684", "5380", "6142", "6973", "7876", "8854", "9910", "11047", "12268", "13576", "14974", "16465", "18052", "19738", "21526" ]
[ "nonn" ]
36
0
2
null
[ "M3385" ]
N. J. A. Sloane, Simon Plouffe
2023-07-14T14:24:53
oeisdata/seq/A006/A006001.seq
02dbec4750f0578c67e768a4badc408e
A006002
a(n) = n*(n+1)^2/2.
[ "0", "2", "9", "24", "50", "90", "147", "224", "324", "450", "605", "792", "1014", "1274", "1575", "1920", "2312", "2754", "3249", "3800", "4410", "5082", "5819", "6624", "7500", "8450", "9477", "10584", "11774", "13050", "14415", "15872", "17424", "19074", "20825", "22680", "24642", "26714", "28899", "31200", "33620", "36162", "38829", "41624" ]
[ "nonn", "nice", "easy" ]
233
0
2
[ "A000217", "A000292", "A000330", "A000914", "A002378", "A002411", "A005449", "A006002", "A014132", "A027480", "A035006", "A045991", "A092364", "A159797", "A163274", "A267370", "A330298" ]
[ "M1920" ]
N. J. A. Sloane
2025-03-31T21:36:35
oeisdata/seq/A006/A006002.seq
20d038a558281b6bd45303020c0e84fb
A006003
a(n) = n*(n^2 + 1)/2.
[ "0", "1", "5", "15", "34", "65", "111", "175", "260", "369", "505", "671", "870", "1105", "1379", "1695", "2056", "2465", "2925", "3439", "4010", "4641", "5335", "6095", "6924", "7825", "8801", "9855", "10990", "12209", "13515", "14911", "16400", "17985", "19669", "21455", "23346", "25345", "27455", "29679", "32020", "34481", "37065", "39775" ]
[ "nonn", "easy", "nice" ]
323
0
3
[ "A000027", "A000292", "A000330", "A000332", "A000447", "A000537", "A000578", "A001620", "A002817", "A004006", "A004068", "A004126", "A004188", "A004466", "A004467", "A005448", "A005449", "A005900", "A005917", "A006003", "A006008", "A006527", "A007588", "A007742", "A011863", "A027480", "A034262", "A037270", "A057587", "A062025", "A063488", "A063521", "A063522", "A063523", "A066886", "A080992", "A105374", "A118465", "A226449", "A248177", "A267017", "A317297", "A325001", "A337886", "A337897", "A337898", "A337960", "A337962" ]
[ "M3849" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:29
oeisdata/seq/A006/A006003.seq
35c07c95914e25ef56cf1c66214ae315
A006004
a(n) = C(n+2,3) + C(n,3) + C(n-1,3).
[ "1", "4", "11", "25", "49", "86", "139", "211", "305", "424", "571", "749", "961", "1210", "1499", "1831", "2209", "2636", "3115", "3649", "4241", "4894", "5611", "6395", "7249", "8176", "9179", "10261", "11425", "12674", "14011", "15439", "16961", "18580", "20299", "22121", "24049", "26086", "28235", "30499", "32881", "35384", "38011", "40765" ]
[ "nonn", "easy", "nice" ]
34
1
2
null
[ "M3412" ]
N. J. A. Sloane
2018-01-22T21:12:03
oeisdata/seq/A006/A006004.seq
a89f97e175d92c53496bf1d070798b67
A006005
The odd prime numbers together with 1.
[ "1", "3", "5", "7", "11", "13", "17", "19", "23", "29", "31", "37", "41", "43", "47", "53", "59", "61", "67", "71", "73", "79", "83", "89", "97", "101", "103", "107", "109", "113", "127", "131", "137", "139", "149", "151", "157", "163", "167", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239", "241", "251", "257", "263", "269", "271" ]
[ "nonn", "easy" ]
55
1
2
[ "A000040", "A002322", "A006005", "A008578", "A065091" ]
null
N. J. A. Sloane
2019-04-15T16:35:13
oeisdata/seq/A006/A006005.seq
a06963497e19ec95e296d468bf6d044f
A006006
Weight distribution of [ 128,29,32 ] 2nd-order Reed-Muller code.
[ "1", "0", "0", "0", "10668", "0", "5291328", "112881664", "300503590", "112881664", "5291328", "0", "10668", "0", "0", "0", "1" ]
[ "nonn", "fini", "full" ]
20
0
5
null
null
N. J. A. Sloane
2023-04-12T11:26:08
oeisdata/seq/A006/A006006.seq
109a043e71c1a4a83f492e631d013d11
A006007
4-dimensional analog of centered polygonal numbers: a(n) = n(n+1)*(n^2+n+4)/12.
[ "0", "1", "5", "16", "40", "85", "161", "280", "456", "705", "1045", "1496", "2080", "2821", "3745", "4880", "6256", "7905", "9861", "12160", "14840", "17941", "21505", "25576", "30200", "35425", "41301", "47880", "55216", "63365", "72385", "82336", "93280", "105281", "118405", "132720", "148296", "165205", "183521" ]
[ "easy", "nonn", "nice" ]
59
0
3
[ "A000217", "A000537", "A000578", "A003215", "A005898", "A006007", "A027602", "A061315", "A061316", "A061318" ]
[ "M3865" ]
N. J. A. Sloane, Simon Plouffe
2023-08-31T15:54:45
oeisdata/seq/A006/A006007.seq
e0486535dac718f966f8e653d60f5364
A006008
Number of inequivalent ways to color vertices of a regular tetrahedron using <= n colors.
[ "0", "1", "5", "15", "36", "75", "141", "245", "400", "621", "925", "1331", "1860", "2535", "3381", "4425", "5696", "7225", "9045", "11191", "13700", "16611", "19965", "23805", "28176", "33125", "38701", "44955", "51940", "59711", "68325", "77841", "88320", "99825", "112421", "126175", "141156", "157435", "175085", "194181", "214800", "237021", "260925", "286595", "314116", "343575" ]
[ "nonn", "easy", "nice" ]
76
0
3
[ "A000332", "A006003", "A006008", "A006550", "A060529", "A144680", "A324999" ]
[ "M3854" ]
N. J. A. Sloane, Clint. C. Williams (Clintwill(AT)aol.com)
2025-02-16T08:32:29
oeisdata/seq/A006/A006008.seq
e81be6504b36ec8ccfce55317051e8d1
A006009
Number of paraffins.
[ "4", "16", "48", "108", "216", "384", "640", "1000", "1500", "2160", "3024", "4116", "5488", "7168", "9216", "11664", "14580", "18000", "22000", "26620", "31944", "38016", "44928", "52728", "61516", "71344", "82320", "94500", "108000", "122880", "139264", "157216", "176868", "198288", "221616", "246924", "274360", "304000", "336000" ]
[ "nonn", "easy" ]
40
1
1
[ "A005994", "A005997", "A006009", "A007009" ]
[ "M3513" ]
N. J. A. Sloane
2024-02-07T11:55:48
oeisdata/seq/A006/A006009.seq
a7556dc0266795d9033c877d7ba83fb6
A006010
Number of paraffins (see Losanitsch reference for precise definition).
[ "1", "5", "20", "52", "117", "225", "400", "656", "1025", "1525", "2196", "3060", "4165", "5537", "7232", "9280", "11745", "14661", "18100", "22100", "26741", "32065", "38160", "45072", "52897", "61685", "71540", "82516", "94725", "108225", "123136", "139520", "157505", "177157", "198612", "221940", "247285", "274721", "304400" ]
[ "nonn", "easy" ]
78
1
2
[ "A005994", "A006010", "A186424", "A317614", "A335648" ]
[ "M3897" ]
N. J. A. Sloane
2022-10-05T05:02:10
oeisdata/seq/A006/A006010.seq
6825399e43515f0edd2889cf919012cd
A006011
a(n) = n^2*(n^2 - 1)/4.
[ "0", "0", "3", "18", "60", "150", "315", "588", "1008", "1620", "2475", "3630", "5148", "7098", "9555", "12600", "16320", "20808", "26163", "32490", "39900", "48510", "58443", "69828", "82800", "97500", "114075", "132678", "153468", "176610", "202275", "230640", "261888", "296208", "333795", "374850", "419580", "468198" ]
[ "nonn", "easy" ]
116
0
3
[ "A000217", "A000290", "A000537", "A001477", "A002415", "A006011", "A008911", "A047928", "A059270", "A074650", "A083374", "A124428", "A126274", "A163932", "A228317" ]
[ "M3044" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:29
oeisdata/seq/A006/A006011.seq
c50ddb7d5012f33ac2a3e4d4f94de86d
A006012
a(0) = 1, a(1) = 2, a(n) = 4*a(n-1) - 2*a(n-2), n >= 2.
[ "1", "2", "6", "20", "68", "232", "792", "2704", "9232", "31520", "107616", "367424", "1254464", "4283008", "14623104", "49926400", "170459392", "581984768", "1987020288", "6784111616", "23162405888", "79081400320", "270000789504", "921840357376", "3147359850496" ]
[ "nonn", "easy" ]
287
0
2
[ "A000079", "A001519", "A003480", "A006012", "A024175", "A030436", "A052961", "A094803", "A140070", "A152252", "A154626", "A265185" ]
[ "M1644" ]
N. J. A. Sloane
2024-12-28T23:15:48
oeisdata/seq/A006/A006012.seq
2f38219e070d275fef5eea9939b9b137
A006013
a(n) = binomial(3*n+1,n)/(n+1).
[ "1", "2", "7", "30", "143", "728", "3876", "21318", "120175", "690690", "4032015", "23841480", "142498692", "859515920", "5225264024", "31983672534", "196947587823", "1219199353190", "7583142491925", "47365474641870", "296983176369495", "1868545312633440", "11793499763070480" ]
[ "nonn", "nice", "easy" ]
358
0
2
[ "A000260", "A006013", "A007318", "A024485", "A047749", "A051255", "A071948", "A092526", "A110616", "A115728", "A121645", "A130564", "A143603", "A236194", "A258708", "A305574" ]
[ "M1782" ]
N. J. A. Sloane
2025-03-19T00:05:09
oeisdata/seq/A006/A006013.seq
6d2aab996d8caa4a93cc3a63c9325280
A006014
a(n+1) = (n+1)*a(n) + Sum_{k=1..n-1} a(k)*a(n-k).
[ "1", "2", "7", "32", "178", "1160", "8653", "72704", "679798", "7005632", "78939430", "965988224", "12762344596", "181108102016", "2748049240573", "44405958742016", "761423731533286", "13809530704348160", "264141249701936818", "5314419112717217792", "112201740111374359516", "2480395343617443024896" ]
[ "nonn", "easy" ]
44
1
2
[ "A006014", "A007814", "A025480", "A073017", "A124758", "A243499", "A284005", "A329369", "A341392" ]
[ "M1790" ]
N. J. A. Sloane
2025-01-10T20:42:55
oeisdata/seq/A006/A006014.seq
f7853e773e0520b96adceea722342c2f
A006015
Nim product 2*n.
[ "0", "2", "3", "1", "8", "10", "11", "9", "12", "14", "15", "13", "4", "6", "7", "5", "32", "34", "35", "33", "40", "42", "43", "41", "44", "46", "47", "45", "36", "38", "39", "37", "48", "50", "51", "49", "56", "58", "59", "57", "60", "62", "63", "61", "52", "54", "55", "53", "16", "18", "19", "17", "24", "26", "27", "25", "28", "30", "31", "29", "20", "22", "23", "21", "128", "130", "131", "129", "136", "138", "139" ]
[ "nonn", "easy", "look" ]
41
0
2
[ "A000695", "A001196", "A004468", "A004480", "A006015", "A051775", "A062880" ]
[ "M0412" ]
N. J. A. Sloane.
2023-03-07T11:54:52
oeisdata/seq/A006/A006015.seq
f0e13aeb66b8ccf9f37c239022df2fb5
A006016
The nim value for the game of Sym with n tails and 1 head.
[ "1", "2", "4", "3", "6", "7", "8", "16", "18", "25", "32", "11", "64", "31", "128", "10", "256", "5", "512", "28", "1024", "34", "2048", "47", "4096", "85" ]
[ "nonn", "more", "changed" ]
31
0
2
null
[ "M0935" ]
N. J. A. Sloane
2025-04-21T03:19:32
oeisdata/seq/A006/A006016.seq
f03b6f7dcb0b76dabeed2ca8126ff2dd
A006017
Nim product 2^n * 2^n.
[ "1", "3", "6", "13", "24", "52", "103", "222", "384", "832", "1648", "3552", "6237", "13563", "26511", "56906", "98304", "212992", "421888", "909312", "1596672", "3472128", "6786816", "14567936", "25190110", "54589881", "108036850", "232800673", "408783316", "888883132" ]
[ "nonn" ]
24
0
2
[ "A006017", "A223541" ]
[ "M2568" ]
N. J. A. Sloane, Jeffrey Shallit
2013-05-24T12:54:31
oeisdata/seq/A006/A006017.seq
36e71dd25599914ef955cf45380a1e8d
A006018
List of periods for game of Third One Lucky.
[ "1", "2", "4", "2", "12", "12", "12", "8", "8", "10", "60", "60", "84", "84", "84", "16", "16", "18", "180", "20", "900", "7200", "7200", "24", "24", "26", "364", "364", "2184" ]
[ "hard", "nonn", "more" ]
49
1
2
null
[ "M0932" ]
N. J. A. Sloane
2024-06-17T15:12:06
oeisdata/seq/A006/A006018.seq
835bbf5199abde1ecf3926ad4d7210a0
A006019
Remoteness number of n in Simon Norton's game of Tribulations.
[ "0", "1", "2", "1", "6", "3", "1", "5", "3", "2", "1", "2", "3", "4", "3", "1", "9", "3", "6", "7", "8", "1", "10", "3", "2", "3", "4", "5", "1", "4", "3", "8", "7", "5", "9", "7", "1", "14", "3", "4", "7", "4", "2", "9", "4", "1", "2", "3", "4", "7", "8", "12", "16", "9", "3", "1", "12", "3", "14", "7", "6", "4", "8", "6", "3", "2", "1", "6", "3", "5", "7", "11", "4" ]
[ "nonn" ]
33
0
3
[ "A006019", "A266726" ]
[ "M0178" ]
N. J. A. Sloane
2018-05-05T02:23:49
oeisdata/seq/A006/A006019.seq
0a5a1f5cd53d45ae9175f81177dd5097
A006020
Suspense numbers for Tribulations.
[ "3", "2", "1", "4", "3", "1", "3", "3", "2", "5", "4", "5", "2", "5", "1", "3", "3", "2", "5", "4", "3", "4", "5", "2", "5", "4", "3", "5", "4", "3", "2", "5", "3", "5", "5", "3", "4", "5", "2", "5", "4", "2", "5", "4", "7", "2", "5", "2", "5", "4", "2", "4", "5", "3", "5", "4", "5", "2", "5", "4", "2", "4", "4", "7", "2", "1", "4", "3", "3", "5", "5", "2", "3", "4", "5" ]
[ "nonn" ]
7
1
1
null
[ "M2237" ]
N. J. A. Sloane.
2012-03-30T16:44:54
oeisdata/seq/A006/A006020.seq
105ff14354d30929f397dab5e4df8702
A006021
The game of contours.
[ "0", "1", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2", "3", "1", "4", "3", "2", "0", "5", "2" ]
[ "nonn" ]
10
0
3
null
[ "M0409" ]
N. J. A. Sloane.
2016-12-14T14:12:26
oeisdata/seq/A006/A006021.seq
c530ccfb8f675585c8f2ea49054e4918
A006022
Sprague-Grundy (or Nim) values for the game of Maundy cake on an n X 1 sheet.
[ "0", "1", "1", "3", "1", "4", "1", "7", "4", "6", "1", "10", "1", "8", "6", "15", "1", "13", "1", "16", "8", "12", "1", "22", "6", "14", "13", "22", "1", "21", "1", "31", "12", "18", "8", "31", "1", "20", "14", "36", "1", "29", "1", "34", "21", "24", "1", "46", "8", "31", "18", "40", "1", "40", "12", "50", "20", "30", "1", "51", "1", "32", "29", "63", "14", "45", "1", "52", "24", "43", "1", "67", "1", "38", "31", "58", "12", "53", "1" ]
[ "nonn" ]
152
1
4
[ "A001348", "A002182", "A006022", "A008864", "A020639", "A027746", "A032742", "A306264", "A306363", "A322034", "A322035", "A322036", "A322382", "A328898", "A328969", "A332993", "A333783", "A333791" ]
[ "M2219" ]
N. J. A. Sloane
2024-08-02T06:26:28
oeisdata/seq/A006/A006022.seq
b55da9fe2d87e5698f991f1751fe729f
A006023
Number of unlabeled mating digraphs with n nodes.
[ "1", "1", "2", "12", "183", "8884", "1495984", "872987584", "1787227218134", "13013640978954744", "341143259362180445672", "32519497484526664873838560", "11366387701006542223325518765872", "14668949294272099348849331250968826816" ]
[ "nonn" ]
29
0
3
[ "A000273", "A004110", "A006023", "A006025" ]
[ "M2046" ]
Simon Plouffe
2019-09-22T08:02:41
oeisdata/seq/A006/A006023.seq
18fe9e8e5f77f4e07baf185d212980e4
A006024
Number of labeled mating graphs with n nodes. Also called point-determining graphs.
[ "1", "1", "1", "4", "32", "588", "21476", "1551368", "218608712", "60071657408", "32307552561088", "34179798520396032", "71474651351939175424", "296572048493274368856832", "2448649084251501449508762880", "40306353989748719650902623919616" ]
[ "nonn" ]
48
0
4
[ "A000311", "A000669", "A006024", "A006025", "A007833", "A079306", "A129583", "A129584", "A129585", "A129586" ]
[ "M3650" ]
Simon Plouffe
2023-02-20T22:08:38
oeisdata/seq/A006/A006024.seq
723106f89f9c0353066fcac0c334aca3
A006025
Number of labeled mating digraphs with n nodes.
[ "1", "1", "3", "54", "3750", "1009680", "1058347920", "4375678520640", "71934792452208000", "4719774805970453006400", "1237727595442264073683462080", "1298006134163762816201615178698880", "5444432200219729912412940250057668378240" ]
[ "nonn" ]
31
0
3
[ "A006024", "A006025" ]
[ "M3160" ]
Simon Plouffe
2019-08-16T15:13:20
oeisdata/seq/A006/A006025.seq
1a371edc7e2dd8e95a0c885ec3621257
A006026
Number of column-convex polyominoes with perimeter n.
[ "1", "3", "12", "54", "260", "1310", "6821", "36413", "198227", "1096259", "6141764", "34784432", "198828308", "1145544680", "6645621536", "38786564126", "227585926704", "1341757498470", "7944249448686", "47217102715624", "281615520373954", "1684957401786580", "10110628493454482", "60830401073611514" ]
[ "nonn", "easy" ]
38
1
2
[ "A006026", "A006027", "A259332", "A259333" ]
[ "M2924" ]
Simon Plouffe
2021-08-22T14:30:55
oeisdata/seq/A006/A006026.seq
e0738cc2b5957c1c8da1fed0b37ce7c1
A006027
Number of directed column-convex polyominoes with perimeter 2n+2.
[ "1", "1", "2", "6", "20", "71", "263", "1005", "3933", "15684", "63505", "260390", "1079019", "4511700", "19011521", "80653480", "344193353", "1476589475", "6364258163", "27545933212", "119676949397", "521739175908", "2281673067934", "10006784399183", "44002280467770", "193957104163645", "856853526774173" ]
[ "nonn" ]
44
1
3
[ "A005435", "A006027" ]
[ "M1647" ]
Simon Plouffe
2021-02-09T06:39:53
oeisdata/seq/A006/A006027.seq
f1624ac66be251701354bf8aff5587fa
A006028
Weight distribution of [ 128,99,8 ] 4th-order Reed-Muller code RM(4,7).
[ "1", "0", "0", "0", "188976", "0", "148157184", "5805342720", "352501184760", "14090340827136", "445990551166720", "11148730324353024", "224814298345622160", "3704888469231108096", "50486579825291883008", "574502111223143792640", "5505259862572668584988" ]
[ "nonn", "fini" ]
13
0
5
[ "A006006", "A006028", "A010083" ]
null
N. J. A. Sloane
2023-08-12T21:13:40
oeisdata/seq/A006/A006028.seq
8261d1aadcefd6d80fdd560edfafd6ea
A006029
Numbers k such that the k-th tetrahedral number k*(k+1)*(k+2)/6 is palindromic.
[ "1", "2", "17", "21", "336" ]
[ "nonn", "base", "more" ]
21
1
2
[ "A006029", "A006030" ]
null
Patrick De Geest
2022-03-01T07:26:03
oeisdata/seq/A006/A006029.seq
645452ffa772f571fb180cd7b3c15e6b
A006030
Palindromic tetrahedral numbers.
[ "1", "4", "969", "1771", "6378736" ]
[ "nonn", "base" ]
5
1
2
[ "A006029", "A006030" ]
null
Patrick De Geest
2024-08-11T14:41:29
oeisdata/seq/A006/A006030.seq
7f3851f9eb05966366102c8f666c957b
A006031
Erroneous version of A016054.
[ "3", "7", "137", "283", "883", "991", "1021", "1193", "3671" ]
[ "dead" ]
5
1
1
null
null
null
2017-06-29T15:33:01
oeisdata/seq/A006/A006031.seq
122652052388be6e1273c240978c75b8
A006032
Numbers k such that (14^k - 1)/13 is prime.
[ "3", "7", "19", "31", "41", "2687", "19697", "59693", "67421", "441697" ]
[ "hard", "nonn", "more" ]
34
1
1
null
[ "M2670" ]
N. J. A. Sloane
2021-12-26T22:09:29
oeisdata/seq/A006/A006032.seq
f7263951371b99375207b04738a7816d
A006033
Numbers n such that (15^n - 1)/14 is prime.
[ "3", "43", "73", "487", "2579", "8741", "37441", "89009", "505117", "639833" ]
[ "nonn", "hard", "more" ]
52
1
1
[ "A003525", "A006033", "A059802", "A062647" ]
[ "M3150" ]
N. J. A. Sloane
2019-04-22T13:51:00
oeisdata/seq/A006/A006033.seq
ff39ae3219182374a09256cf3ff2d32f
A006034
Numbers n such that (17^n-1)/16 is prime.
[ "3", "5", "7", "11", "47", "71", "419", "4799", "35149", "54919", "74509", "1990523" ]
[ "hard", "nonn", "more" ]
27
1
1
null
[ "M2415" ]
N. J. A. Sloane
2020-08-03T08:50:57
oeisdata/seq/A006/A006034.seq
6ed0ee813d1340035852c9f36d44c1a2
A006035
Numbers n such that (19^n-1)/18 is prime.
[ "19", "31", "47", "59", "61", "107", "337", "1061", "9511", "22051", "209359" ]
[ "nonn", "more" ]
35
1
1
null
[ "M5072" ]
N. J. A. Sloane
2018-09-10T13:29:03
oeisdata/seq/A006/A006035.seq
3dec8ba044e56c9ade36bf15bf69bf70
A006036
Primitive pseudoperfect numbers.
[ "6", "20", "28", "88", "104", "272", "304", "350", "368", "464", "490", "496", "550", "572", "650", "748", "770", "910", "945", "1184", "1190", "1312", "1330", "1376", "1430", "1504", "1575", "1610", "1696", "1870", "1888", "1952", "2002", "2030", "2090", "2170", "2205", "2210", "2470", "2530", "2584", "2590", "2870", "2990", "3010", "3128", "3190", "3230", "3290", "3410", "3465", "3496", "3710", "3770", "3944", "4070", "4095", "4130", "4216", "4270", "4288", "4408", "4510", "4544", "4672", "4690", "4712", "4730", "4970" ]
[ "nonn", "nice" ]
43
1
1
[ "A005835", "A006036", "A027751", "A210455" ]
[ "M4133" ]
N. J. A. Sloane, R. K. Guy
2025-02-16T08:32:29
oeisdata/seq/A006/A006036.seq
8b6e7adbc6d47d9bd0a4ef881465b74d
A006037
Weird numbers: abundant (A005101) but not pseudoperfect (A005835).
[ "70", "836", "4030", "5830", "7192", "7912", "9272", "10430", "10570", "10792", "10990", "11410", "11690", "12110", "12530", "12670", "13370", "13510", "13790", "13930", "14770", "15610", "15890", "16030", "16310", "16730", "16870", "17272", "17570", "17990", "18410", "18830", "18970", "19390", "19670" ]
[ "nonn", "nice" ]
167
1
1
[ "A002975", "A005100", "A005101", "A005835", "A006037", "A087167", "A138850", "A210455" ]
[ "M5339" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006037.seq
b9ef015f59b311a214df2c7787c027ab
A006038
Odd primitive abundant numbers.
[ "945", "1575", "2205", "3465", "4095", "5355", "5775", "5985", "6435", "6825", "7245", "7425", "8085", "8415", "8925", "9135", "9555", "9765", "11655", "12705", "12915", "13545", "14805", "15015", "16695", "18585", "19215", "19635", "21105", "21945", "22365", "22995", "23205", "24885", "25935", "26145", "26565", "28035", "28215" ]
[ "nonn" ]
72
1
1
[ "A000203", "A005101", "A005231", "A006038", "A027751", "A091191", "A379949" ]
[ "M5486" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006038.seq
90d4664b81791bb5055f28e4dc55e2df
A006039
Primitive non-deficient numbers.
[ "6", "20", "28", "70", "88", "104", "272", "304", "368", "464", "496", "550", "572", "650", "748", "836", "945", "1184", "1312", "1376", "1430", "1504", "1575", "1696", "1870", "1888", "1952", "2002", "2090", "2205", "2210", "2470", "2530", "2584", "2990", "3128", "3190", "3230", "3410", "3465", "3496", "3770", "3944", "4030" ]
[ "nonn" ]
54
1
1
[ "A000396", "A001065", "A005101", "A006038", "A006039", "A023196", "A071395", "A091191", "A180332", "A333967", "A337479", "A337688", "A337689", "A337690", "A337691", "A337814", "A338133", "A338427", "A341619", "A341620", "A342669", "A352739" ]
[ "M4132" ]
N. J. A. Sloane, R. K. Guy
2022-11-29T12:53:15
oeisdata/seq/A006/A006039.seq
45edbe9c442c27c1b0b92504b4f378b9
A006040
a(n) = Sum_{i=0..n} (n!/(n-i)!)^2.
[ "1", "2", "9", "82", "1313", "32826", "1181737", "57905114", "3705927297", "300180111058", "30018011105801", "3632179343801922", "523033825507476769", "88392716510763573962", "17324972436109660496553", "3898118798124673611724426", "997918412319916444601453057", "288398421160455852489819933474" ]
[ "nonn", "easy" ]
43
0
2
[ "A006040", "A073701", "A099597" ]
[ "M1950" ]
N. J. A. Sloane, Simon Plouffe
2023-10-08T04:52:40
oeisdata/seq/A006/A006040.seq
0f5583609ac5758b3403322133c802b6
A006041
a(n+1) = (n^2 - 1)*a(n) + n + 1.
[ "0", "2", "9", "76", "1145", "27486", "962017", "46176824", "2909139921", "232731193690", "23040388175321", "2764846581038532", "395373061088510089", "66422674262869694966", "12952421481259590518385", "2901342411802148276118256", "739842315009547810410155297", "213074586722749769398124725554", "68823091511448175515594286353961" ]
[ "nonn", "easy" ]
25
1
2
null
[ "M1949" ]
N. J. A. Sloane, Simon Plouffe
2020-05-16T14:36:59
oeisdata/seq/A006/A006041.seq
af2adca3e94f178512e65400c0515e4e
A006042
The nim-square of n.
[ "0", "1", "3", "2", "6", "7", "5", "4", "13", "12", "14", "15", "11", "10", "8", "9", "24", "25", "27", "26", "30", "31", "29", "28", "21", "20", "22", "23", "19", "18", "16", "17", "52", "53", "55", "54", "50", "51", "49", "48", "57", "56", "58", "59", "63", "62", "60", "61", "44", "45", "47", "46", "42", "43", "41", "40", "33", "32", "34", "35", "39", "38", "36", "37", "103", "102", "100", "101", "97", "96", "98", "99" ]
[ "nonn", "nice", "easy", "look" ]
57
0
3
[ "A006017", "A006042", "A051775", "A051776", "A051917", "A160679", "A212200", "A335162", "A335170", "A335171", "A335172", "A335173", "A335535", "A335536" ]
[ "M2251" ]
N. J. A. Sloane
2023-08-04T01:40:54
oeisdata/seq/A006/A006042.seq
2de9f50026d78802fdaa1a0060dd3595
A006043
A traffic light problem: expansion of 2/(1 - 3*x)^3.
[ "2", "18", "108", "540", "2430", "10206", "40824", "157464", "590490", "2165130", "7794468", "27634932", "96722262", "334807830", "1147912560", "3902902704", "13172296626", "44165935746", "147219785820", "488149816140", "1610894393262", "5292938720718", "17322344904168", "56485907296200", "183579198712650", "594796603828986" ]
[ "nonn", "easy" ]
71
0
1
[ "A000142", "A000217", "A000244", "A006043", "A006044", "A027472", "A116138", "A152818", "A154120" ]
[ "M2107" ]
N. J. A. Sloane, Simon Plouffe
2023-01-08T02:39:40
oeisdata/seq/A006/A006043.seq
5091a061543a64930ca900ba685332c3
A006044
a(n) = 4^(n-4)*(n-1)*(n-2)*(n-3).
[ "6", "96", "960", "7680", "53760", "344064", "2064384", "11796480", "64880640", "346030080", "1799356416", "9160359936", "45801799680", "225485783040", "1095216660480", "5257039970304", "24970939858944", "117510305218560", "548381424353280", "2539871860162560", "11683410556747776", "53409876830846976" ]
[ "nonn", "easy" ]
63
4
1
[ "A000142", "A006043", "A006044", "A038846", "A152818", "A154120" ]
[ "M4290" ]
N. J. A. Sloane
2023-01-08T02:39:53
oeisdata/seq/A006/A006044.seq
255bea5a94612c9575ae4c2be91a2b40
A006045
Sum of orders of all 2 X 2 matrices with entries mod n.
[ "1", "26", "272", "722", "5270", "5260", "37358", "18414", "56216", "95668", "487714", "99796", "1304262", "627046", "593398", "481982", "7044222", "931396", "11570384", "1602940", "4037650", "8694134", "40220524", "2069292", "15855230", "21686124", "13215872", "10948486", "129952894", "10451648" ]
[ "nonn" ]
38
1
2
null
[ "M3946" ]
N. J. A. Sloane, Albert Wilansky
2021-01-28T21:35:49
oeisdata/seq/A006/A006045.seq
db3f5cc0d4e2e41274133a1b2240f18e
A006046
Total number of odd entries in first n rows of Pascal's triangle: a(0) = 0, a(1) = 1, a(2k) = 3*a(k), a(2k+1) = 2*a(k) + a(k+1). a(n) = Sum_{i=0..n-1} 2^wt(i).
[ "0", "1", "3", "5", "9", "11", "15", "19", "27", "29", "33", "37", "45", "49", "57", "65", "81", "83", "87", "91", "99", "103", "111", "119", "135", "139", "147", "155", "171", "179", "195", "211", "243", "245", "249", "253", "261", "265", "273", "281", "297", "301", "309", "317", "333", "341", "357", "373", "405", "409", "417", "425", "441", "449", "465", "481", "513", "521" ]
[ "nonn", "nice", "easy", "look" ]
219
0
3
[ "A000027", "A001316", "A006046", "A038183", "A048896", "A064194", "A073121", "A074330", "A080263", "A080978", "A116520", "A130665", "A159912", "A166556", "A268524", "A268525", "A268526", "A268527", "A360189" ]
[ "M2445" ]
Jeffrey Shallit
2025-02-16T08:32:29
oeisdata/seq/A006/A006046.seq
196b7affc8e0f8ce870a4b20b32da396
A006047
Number of entries in n-th row of Pascal's triangle not divisible by 3.
[ "1", "2", "3", "2", "4", "6", "3", "6", "9", "2", "4", "6", "4", "8", "12", "6", "12", "18", "3", "6", "9", "6", "12", "18", "9", "18", "27", "2", "4", "6", "4", "8", "12", "6", "12", "18", "4", "8", "12", "8", "16", "24", "12", "24", "36", "6", "12", "18", "12", "24", "36", "18", "36", "54", "3", "6", "9", "6", "12", "18", "9", "18", "27", "6", "12", "18", "12", "24", "36", "18", "36", "54", "9", "18", "27", "18", "36", "54", "27", "54" ]
[ "nonn", "changed" ]
116
0
2
[ "A001316", "A003586", "A006047", "A038148", "A053735", "A083093", "A089898", "A206424", "A227428", "A286586", "A286587", "A286633" ]
[ "M0422" ]
Jeffrey Shallit
2025-04-25T12:54:18
oeisdata/seq/A006/A006047.seq
84c0f34d0c08566a6481a98cc73de91e
A006048
Number of entries in first n rows of Pascal's triangle not divisible by 3.
[ "1", "3", "6", "8", "12", "18", "21", "27", "36", "38", "42", "48", "52", "60", "72", "78", "90", "108", "111", "117", "126", "132", "144", "162", "171", "189", "216", "218", "222", "228", "232", "240", "252", "258", "270", "288", "292", "300", "312", "320", "336", "360", "372", "396", "432", "438", "450", "468", "480", "504", "540", "558", "594", "648", "651", "657", "666", "672", "684", "702", "711", "729", "756", "762", "774", "792", "804", "828", "864", "882", "918", "972", "981", "999", "1026", "1044", "1080", "1134", "1161", "1215", "1296" ]
[ "nonn", "changed" ]
35
0
2
[ "A006047", "A006048" ]
[ "M2519" ]
Jeffrey Shallit
2025-04-23T20:31:39
oeisdata/seq/A006/A006048.seq
c2550627c07abe6b054405542052d46d
A006049
Numbers k such that k and k+1 have the same number of distinct prime divisors.
[ "2", "3", "4", "7", "8", "14", "16", "20", "21", "31", "33", "34", "35", "38", "39", "44", "45", "50", "51", "54", "55", "56", "57", "62", "68", "74", "75", "76", "85", "86", "87", "91", "92", "93", "94", "95", "98", "99", "111", "115", "116", "117", "118", "122", "123", "127", "133", "134", "135", "141", "142", "143", "144", "145", "146", "147", "152", "158", "159", "160", "161", "171", "175" ]
[ "nonn", "easy", "nice" ]
48
1
1
[ "A001221", "A006049", "A006073", "A052215", "A062974", "A107800", "A294277", "A294278" ]
null
N. J. A. Sloane
2024-09-17T04:04:03
oeisdata/seq/A006/A006049.seq
298a38bc7798455c930483d5807fb5d7
A006050
Smallest number of additive persistence n.
[ "0", "10", "19", "199", "19999999999999999999999" ]
[ "nonn", "base", "nice" ]
34
0
2
[ "A003001", "A006050", "A031286", "A045646" ]
[ "M4683" ]
N. J. A. Sloane
2025-03-10T11:50:50
oeisdata/seq/A006/A006050.seq
ae6a478c627f5ed6d463c32ba4669188
A006051
Square hex numbers.
[ "1", "169", "32761", "6355441", "1232922769", "239180661721", "46399815451081", "9001325016847969", "1746210653453054881", "338755865444875798921", "65716891685652451935769", "12748738231151130799740241", "2473189499951633722697670961", "479786014252385791072548426169" ]
[ "nonn", "easy" ]
62
1
2
[ "A000290", "A001570", "A001922", "A003215", "A003500", "A006051" ]
[ "M5409" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006051.seq
a1d34f0c73092f401a0c5d18a39c4f33
A006052
Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections.
[ "1", "0", "1", "880", "275305224", "17753889197660635632" ]
[ "nonn", "hard", "nice", "more" ]
121
1
4
[ "A006052", "A270876", "A271103", "A271104" ]
[ "M5482" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006052.seq
1ea2642dde262d92960c378c1888c08d
A006053
a(n) = a(n-1) + 2*a(n-2) - a(n-3), with a(0) = a(1) = 0, a(2) = 1.
[ "0", "0", "1", "1", "3", "4", "9", "14", "28", "47", "89", "155", "286", "507", "924", "1652", "2993", "5373", "9707", "17460", "31501", "56714", "102256", "184183", "331981", "598091", "1077870", "1942071", "3499720", "6305992", "11363361", "20475625", "36896355", "66484244", "119801329", "215873462", "388991876", "700937471" ]
[ "nonn", "easy" ]
203
0
5
[ "A006053", "A006054", "A052547", "A077865", "A094789", "A094790", "A096975", "A096976", "A120757", "A187065", "A187066", "A187067", "A214683", "A215076", "A215100" ]
[ "M2358" ]
N. J. A. Sloane
2025-01-22T09:23:43
oeisdata/seq/A006/A006053.seq
7d02189b0d8299f73c5695a80b6a956f
A006054
a(n) = 2*a(n-1) + a(n-2) - a(n-3), with a(0) = a(1) = 0, a(2) = 1.
[ "0", "0", "1", "2", "5", "11", "25", "56", "126", "283", "636", "1429", "3211", "7215", "16212", "36428", "81853", "183922", "413269", "928607", "2086561", "4688460", "10534874", "23671647", "53189708", "119516189", "268550439", "603427359", "1355888968", "3046654856", "6845771321", "15382308530", "34563733525" ]
[ "nonn", "easy" ]
189
0
4
[ "A005578", "A006053", "A006054", "A006356", "A007583", "A080937", "A094790", "A144159", "A180264", "A214683", "A214699", "A214779", "A215112", "A306334" ]
[ "M1396" ]
N. J. A. Sloane
2023-08-20T10:48:45
oeisdata/seq/A006/A006054.seq
ab0a9e525367cb7fd6d80ad512216143
A006055
Primes with consecutive (ascending) digits.
[ "2", "3", "5", "7", "23", "67", "89", "4567", "78901", "678901", "23456789", "45678901", "9012345678901", "789012345678901", "56789012345678901234567890123", "90123456789012345678901234567", "678901234567890123456789012345678901" ]
[ "nonn", "base" ]
55
1
1
[ "A006055", "A048398", "A052016", "A052017", "A120804", "A120805" ]
[ "M0679" ]
N. J. A. Sloane, Richard C. Schroeppel
2025-02-16T08:32:29
oeisdata/seq/A006/A006055.seq
19cdc27d6e12c3af47b920eaada939eb
A006056
Number of topologies on n labeled points satisfying the T_4 axiom.
[ "1", "1", "4", "26", "255", "3642", "75606", "2316169", "106289210", "7321773414", "748425136289", "111576624613588", "23864968806932886", "7225895692327786931", "3064182503223082011556", "1803904252801640389374494", "1463405916763710662849541695", "1625522872429294851288338156654" ]
[ "nonn", "nice" ]
28
0
3
[ "A000110", "A000798", "A001035", "A001927", "A001929", "A006056", "A006057", "A006058", "A006059" ]
[ "M3615" ]
N. J. A. Sloane
2017-10-29T21:40:19
oeisdata/seq/A006/A006056.seq
0bf0780b9caf4724bf68ffdc4f11d95c
A006057
Number of topologies on n labeled points satisfying axioms T_0-T_4.
[ "1", "1", "3", "16", "137", "1826", "37777", "1214256", "60075185", "4484316358", "493489876721", "78456654767756", "17735173202222665", "5630684018989523274", "2486496790249207981169", "1515191575312017416011456" ]
[ "nonn", "nice" ]
37
0
3
[ "A000110", "A000798", "A001035", "A001927", "A001929", "A006056", "A006057", "A006058", "A006059" ]
[ "M3028" ]
N. J. A. Sloane
2019-04-08T03:48:12
oeisdata/seq/A006/A006057.seq
c91d450d15811ca8535ebe9fc330d14d
A006058
Number of connected labeled T_4-topologies with n points.
[ "1", "1", "3", "16", "145", "2111", "47624", "1626003", "82564031", "6146805142", "662718022355", "102336213875523", "22408881211102698", "6895949927379360277", "2958271314760111914191", "1756322140048351303019576" ]
[ "nonn", "nice" ]
31
0
3
[ "A000110", "A000798", "A001035", "A001927", "A001929", "A001930", "A003465", "A006056", "A006057", "A006058", "A006059", "A108798", "A306445", "A326878", "A326906" ]
[ "M3030" ]
N. J. A. Sloane
2020-01-01T15:21:30
oeisdata/seq/A006/A006058.seq
6b57c5a64a43e723f0e2ff48426a26ed
A006059
Number of connected labeled T_0-T_4-topologies with n points.
[ "1", "1", "2", "9", "76", "1095", "25386", "910161", "49038872", "3885510411", "445110425110", "72721717736613", "16755380125270788", "5393244363726095487", "2405910197342218830914", "1477264863856923105482745", "1241074736327051013648799024", "1419169006353332682835352361843" ]
[ "nonn", "nice" ]
27
0
3
[ "A000110", "A000798", "A001035", "A001927", "A001929", "A006056", "A006057", "A006058", "A006059" ]
[ "M1948" ]
N. J. A. Sloane
2019-12-30T13:23:52
oeisdata/seq/A006/A006059.seq
f9fec6d6ac201b0329e7f54ffa46aefd
A006060
Triangular star numbers.
[ "1", "253", "49141", "9533161", "1849384153", "358770992581", "69599723176621", "13501987525271953", "2619315980179582321", "508133798167313698381", "98575337528478677903653", "19123107346726696199610361" ]
[ "nonn" ]
45
1
2
[ "A000567", "A003154", "A006060", "A006061", "A051673" ]
[ "M5425" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006060.seq
127bc98a64ac2b83b5e402696dd07b6a
A006061
Star numbers (A003154) that are squares.
[ "1", "121", "11881", "1164241", "114083761", "11179044361", "1095432263641", "107341182792481", "10518340481399521", "1030690025994360601", "100997104206965939401", "9896685522256667700721", "969774184076946468731281" ]
[ "nonn", "easy" ]
51
1
2
[ "A003154", "A006061", "A007667", "A054320" ]
[ "M5385" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006061.seq
820b740c1804669ef12902deb6db639d
A006062
Star-hex numbers.
[ "1", "37", "1261", "42841", "1455337", "49438621", "1679457781", "57052125937", "1938092824081", "65838103892821", "2236557439531837", "75977114840189641", "2580985347126915961", "87677524687474953037", "2978454854027021487301", "101179787512231255615201", "3437134320561835669429537" ]
[ "nonn", "easy" ]
52
1
2
[ "A001109", "A001652", "A001653", "A006062", "A046090" ]
[ "M5265" ]
N. J. A. Sloane, Jul 11 1991
2024-09-02T08:38:02
oeisdata/seq/A006/A006062.seq
f840479e1e34a9557e0f11f01ef461ae
A006063
A card-arranging problem: values of n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a cube for every i.
[ "7", "19", "26", "37", "44", "56", "63", "66", "68", "80", "82", "85", "87", "98", "100", "103", "105", "110", "112", "115", "116", "117", "118", "119", "120", "121", "122", "123", "124", "125", "126", "127", "128", "129", "130", "131", "132", "133", "135", "147", "149", "150", "151", "152", "155", "156", "159", "171", "173", "174", "175", "176", "177", "178", "179" ]
[ "nonn" ]
19
1
1
[ "A006063", "A095986", "A096680" ]
[ "M4361" ]
N. J. A. Sloane
2018-08-28T10:46:04
oeisdata/seq/A006/A006063.seq
77783f14815e856cd278fca596d7d632
A006064
Smallest junction number with n generators.
[ "0", "101", "10000000000001", "1000000000000000000000102" ]
[ "nonn", "base" ]
83
1
2
[ "A003052", "A006064", "A230093", "A230100", "A230303", "A230638", "A230640", "A230857", "A230867", "A238840", "A238841", "A238842", "A238843" ]
[ "M5367" ]
N. J. A. Sloane.
2025-03-26T08:46:09
oeisdata/seq/A006/A006064.seq
a0b96450ff67fc80cfa6c48cba4acaad
A006065
Maximal number of 4-tree rows in n-tree orchard problem.
[ "0", "0", "0", "1", "1", "1", "2", "2", "3", "5", "6", "7", "9", "10", "12", "15", "16", "18", "20", "23" ]
[ "nonn", "hard", "nice", "more" ]
92
1
7
[ "A003035", "A006065", "A008997", "A172992" ]
[ "M0290" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006065.seq
459e8317f792bfb58d6ebe126f7228b6
A006066
Kobon triangles: maximal number of nonoverlapping triangles that can be formed from n lines drawn in the plane.
[ "0", "0", "1", "2", "5", "7", "11", "15", "21", "25" ]
[ "nonn", "hard", "more" ]
110
1
4
null
[ "M1334" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006066.seq
350ee248d3caed386804378271c1fe39
A006067
Number of ways to quarter an n X n chessboard.
[ "1", "1", "1", "5", "7", "37", "104", "766", "3970", "43318", "431932", "7695805", "137066448", "4015896016", "128095791922", "6371333036059", "355704307903818", "30153126159555641", "2952926822418475378", "431453249608567040694", "73569487283165427567144", "18558756256964594960321428" ]
[ "nonn", "nice" ]
32
1
4
[ "A006067", "A064941", "A257952", "A272070" ]
[ "M3769" ]
N. J. A. Sloane
2016-11-19T19:25:34
oeisdata/seq/A006/A006067.seq
b889d15a4355f63eb5ab6b9ac30d092b
A006068
a(n) is Gray-coded into n.
[ "0", "1", "3", "2", "7", "6", "4", "5", "15", "14", "12", "13", "8", "9", "11", "10", "31", "30", "28", "29", "24", "25", "27", "26", "16", "17", "19", "18", "23", "22", "20", "21", "63", "62", "60", "61", "56", "57", "59", "58", "48", "49", "51", "50", "55", "54", "52", "53", "32", "33", "35", "34", "39", "38", "36", "37", "47", "46", "44", "45", "40", "41", "43", "42", "127", "126", "124", "125", "120", "121" ]
[ "nonn", "easy", "nice", "look", "hear" ]
120
0
3
[ "A000079", "A003100", "A003188", "A003987", "A005811", "A006068", "A010060", "A014550", "A038554", "A054429", "A055975", "A180200", "A209281" ]
[ "M2253" ]
N. J. A. Sloane
2024-08-04T11:48:32
oeisdata/seq/A006/A006068.seq
3738e6fbbc35c2224125d95248796e98
A006069
Number of directed Hamiltonian cycles (or Gray codes) on n-cube with a marked starting node.
[ "2", "8", "96", "43008", "58018928640", "4587291356489073135452160" ]
[ "nonn", "more" ]
42
1
1
[ "A003042", "A006069", "A006070", "A091299", "A091302", "A159344" ]
[ "M1903" ]
N. J. A. Sloane.
2025-02-16T08:32:29
oeisdata/seq/A006/A006069.seq
0ec37bc893cf15053d804a2fd2bbece8
A006070
Number of Hamiltonian paths on n-cube which are strictly not cycles.
[ "0", "0", "48", "48384", "129480729600" ]
[ "nonn", "hard", "more" ]
22
1
3
[ "A006069", "A006070", "A091299" ]
[ "M5295" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006070.seq
2b9e77e3f9c02082770ed13e803f7423
A006071
Maximal length of rook tour on an n X n board.
[ "1", "4", "14", "38", "76", "136", "218", "330", "472", "652", "870", "1134", "1444", "1808", "2226", "2706", "3248", "3860", "4542", "5302", "6140", "7064", "8074", "9178", "10376", "11676", "13078", "14590", "16212", "17952", "19810", "21794", "23904", "26148", "28526", "31046", "33708", "36520", "39482", "42602" ]
[ "nonn", "walk" ]
26
1
2
[ "A006071", "A152100", "A152110", "A152132", "A152135" ]
[ "M3474" ]
N. J. A. Sloane
2023-07-14T14:34:08
oeisdata/seq/A006/A006071.seq
3ddfb3ea14e73e4956730bd9be07a8c4
A006072
Numbers with mirror symmetry about middle.
[ "0", "1", "8", "11", "88", "101", "111", "181", "808", "818", "888", "1001", "1111", "1881", "8008", "8118", "8888", "10001", "10101", "10801", "11011", "11111", "11811", "18081", "18181", "18881", "80008", "80108", "80808", "81018", "81118", "81818", "88088", "88188", "88888", "100001", "101101", "108801", "110011", "111111", "118811", "180081" ]
[ "base", "nonn", "easy", "changed" ]
62
1
3
[ "A000787", "A006072", "A045574" ]
[ "M4481" ]
N. J. A. Sloane.
2025-04-27T14:49:01
oeisdata/seq/A006/A006072.seq
bfcd80347a9c0a5dd1e9dd10f61264c2
A006073
Numbers k such that k, k+1 and k+2 all have the same number of distinct prime divisors.
[ "2", "3", "7", "20", "33", "34", "38", "44", "50", "54", "55", "56", "74", "75", "85", "86", "91", "92", "93", "94", "98", "115", "116", "117", "122", "133", "134", "141", "142", "143", "144", "145", "146", "158", "159", "160", "175", "176", "183", "187", "200", "201", "205", "206", "207", "212", "213", "214", "215", "216", "217", "224", "235", "247" ]
[ "nonn" ]
29
1
1
[ "A001221", "A006049", "A006073", "A045932" ]
null
N. J. A. Sloane
2024-06-12T18:49:44
oeisdata/seq/A006/A006073.seq
49eec1ffd9e15752bbd8f0bd28e60384
A006074
Number of polyaboloes (or polytans): number of different shapes that can be formed with n congruent isosceles right triangles, identifying mirror images.
[ "1", "3", "4", "14", "30", "107", "318", "1116", "3743", "13240", "46476", "166358", "596638", "2158829", "7839845", "28616815", "104814161", "385269397", "1420242629", "5249877583", "19452536934", "72237904034" ]
[ "nonn", "nice", "hard", "more" ]
64
1
2
[ "A006074", "A151519", "A245676" ]
[ "M2379" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006074.seq
eafe2e4aa24cced4049039bfca111e85
A006075
Minimal number of knights needed to cover an n X n board.
[ "1", "4", "4", "4", "5", "8", "10", "12", "14", "16", "21", "24", "28", "32", "36", "40", "46", "52", "57", "62", "68" ]
[ "nonn", "hard", "more", "nice" ]
61
1
2
[ "A006075", "A006076", "A075458", "A075561", "A103315", "A189889", "A342576" ]
[ "M3224" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006075.seq
d9ed69000f177cada8dba25520fa9c43
A006076
Sequence A006075 gives minimal number of knights needed to cover an n X n board. This sequence gives number of inequivalent solutions using A006075(n) knights.
[ "1", "1", "2", "3", "8", "23", "3", "1", "1", "2", "100", "1", "20", "1", "63", "1", "29", "2551" ]
[ "nonn", "hard", "nice" ]
43
1
3
[ "A006075", "A006076", "A098604", "A103315" ]
[ "M0884" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006076.seq
da02522ec3af69b9a79852747d8e54ac
A006077
(n+1)^2*a(n+1) = (9n^2+9n+3)*a(n) - 27*n^2*a(n-1), with a(0) = 1 and a(1) = 3.
[ "1", "3", "9", "21", "9", "-297", "-2421", "-12933", "-52407", "-145293", "-35091", "2954097", "25228971", "142080669", "602217261", "1724917221", "283305033", "-38852066421", "-337425235479", "-1938308236731", "-8364863310291", "-24286959061533", "-3011589296289", "574023003011199", "5028616107443691" ]
[ "sign" ]
140
0
2
[ "A000172", "A000984", "A002893", "A002895", "A005258", "A005259", "A005260", "A006077", "A036917", "A063007", "A081085", "A091401", "A093388", "A125143", "A133370", "A143003", "A143007", "A143413", "A143414", "A143415", "A143583", "A183204", "A214262", "A219692", "A226535", "A227216", "A227454", "A229111", "A260667", "A260793", "A260832", "A262177", "A264541", "A264542", "A268545", "A268555", "A279619", "A290575", "A290576", "A291275", "A291284" ]
[ "M2775" ]
N. J. A. Sloane
2023-06-15T06:30:31
oeisdata/seq/A006/A006077.seq
2b6f23058d415ffef0bc4a22057d9305
A006078
Number of triangulated (n+2)-gons rooted at an exterior edge.
[ "1", "1", "5", "12", "45", "143", "511", "1768", "6330", "22610", "81818", "297160", "1086813", "3991995", "14733435", "54587280", "203000094", "757398510", "2834519142", "10637507400", "40023665682", "150946230006", "570534682710", "2160865067312", "8199711750100" ]
[ "nonn", "easy", "nice" ]
39
2
3
null
[ "M3822" ]
N. J. A. Sloane, E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk)
2019-02-18T12:59:31
oeisdata/seq/A006/A006078.seq
eb227d690ce9b5a6411717a04513fc23
A006079
Number of asymmetric planted projective plane trees with n+1 nodes; bracelets (reversible necklaces) with n black beads and n-1 white beads.
[ "1", "1", "0", "1", "4", "16", "56", "197", "680", "2368", "8272", "29162", "103544", "370592", "1335504", "4844205", "17672400", "64810240", "238795040", "883585406", "3281967832", "12232957152", "45740929104", "171529130786", "644950721584", "2430970600576", "9183671335776", "34766765428852", "131873955816880" ]
[ "nonn", "nice", "easy" ]
57
1
5
[ "A000029", "A000031", "A000108", "A001405", "A006079", "A006080", "A006081", "A006082" ]
[ "M3515" ]
N. J. A. Sloane
2023-09-04T23:37:41
oeisdata/seq/A006/A006079.seq
ce5814b8d869e0350235d50802155de6
A006080
Number of rooted projective plane trees with n nodes.
[ "1", "1", "2", "4", "9", "21", "56", "155", "469", "1480", "4882", "16545", "57384", "202060", "720526", "2593494", "9408469", "34350507", "126109784", "465200333", "1723346074", "6408356210", "23911272090", "89495909409", "335916761128", "1264114452996", "4768464309416", "18027250459483", "68291947831046", "259200707489634" ]
[ "nonn", "nice" ]
30
1
3
[ "A006079", "A006080", "A006081", "A006082" ]
[ "M1188" ]
N. J. A. Sloane
2021-12-17T11:28:38
oeisdata/seq/A006/A006080.seq
cec9bda33eaacb292983e9e7249ec324
A006081
Number of line-rooted projective plane trees with n nodes.
[ "1", "1", "3", "6", "17", "44", "133", "404", "1319", "4392", "15114", "52796", "187410", "671848", "2430509", "8852584", "32438603", "119463056", "441926206", "1641246060", "6117011262", "22871513128", "85766691938", "322479555096", "1215493792902", "4591852445104", "17383416640308", "65937045017304" ]
[ "nonn", "easy", "nice" ]
33
2
3
[ "A000108", "A001405", "A006081" ]
[ "M2593" ]
N. J. A. Sloane
2019-02-18T13:10:23
oeisdata/seq/A006/A006081.seq
af321485abc69e4dcc07955eb67388ce
A006082
Number of labeled projective plane trees (or "flat" trees) with n nodes.
[ "1", "1", "1", "2", "3", "6", "12", "27", "65", "175", "490", "1473", "4588", "14782", "48678", "163414", "555885", "1913334", "6646728", "23278989", "82100014", "291361744", "1039758962", "3729276257", "13437206032", "48620868106", "176611864312", "643834562075", "2354902813742", "8640039835974", "31791594259244" ]
[ "nonn" ]
73
1
4
[ "A001405", "A002995", "A006079", "A006080", "A006081", "A006082", "A126120", "A185100", "A302828", "A303929" ]
[ "M0798" ]
N. J. A. Sloane
2024-03-21T21:09:57
oeisdata/seq/A006/A006082.seq
b6342d7b46c16ee5e0ff915d12342137
A006083
Continued fraction for e/2.
[ "1", "2", "1", "3", "1", "1", "1", "3", "3", "3", "1", "3", "1", "3", "5", "3", "1", "5", "1", "3", "7", "3", "1", "7", "1", "3", "9", "3", "1", "9", "1", "3", "11", "3", "1", "11", "1", "3", "13", "3", "1", "13", "1", "3", "15", "3", "1", "15", "1", "3", "17", "3", "1", "17", "1", "3", "19", "3", "1", "19", "1", "3", "21", "3", "1", "21", "1", "3", "23", "3", "1", "23", "1", "3", "25", "3", "1", "25", "1", "3", "27", "3", "1", "27", "1", "3", "29", "3", "1", "29", "1", "3", "31", "3" ]
[ "cofr", "nonn", "easy" ]
35
1
2
[ "A006083", "A019739" ]
[ "M0125" ]
N. J. A. Sloane, Jeffrey Shallit
2016-05-17T04:04:38
oeisdata/seq/A006/A006083.seq
ca4f6973c784b4afba3ae7de448f5dc2
A006084
Continued fraction for e/3.
[ "0", "1", "9", "1", "1", "1", "5", "1", "1", "1", "1", "26", "1", "1", "3", "5", "1", "3", "1", "1", "44", "1", "1", "5", "5", "1", "5", "1", "1", "62", "1", "1", "7", "5", "1", "7", "1", "1", "80", "1", "1", "9", "5", "1", "9", "1", "1", "98", "1", "1", "11", "5", "1", "11", "1", "1", "116", "1", "1", "13", "5", "1", "13", "1", "1", "134", "1", "1", "15", "5", "1", "15", "1", "1", "152", "1", "1", "17", "5", "1", "17", "1", "1", "170", "1", "1", "19", "5", "1", "19", "1", "1" ]
[ "nonn", "cofr", "easy" ]
27
1
3
[ "A006084", "A019740" ]
[ "M4591" ]
N. J. A. Sloane, Jeffrey Shallit
2016-05-17T05:36:43
oeisdata/seq/A006/A006084.seq
45547d7801774e3b8aac0e2ba3daa0d9
A006085
Continued fraction for e/4.
[ "0", "1", "2", "8", "3", "1", "1", "1", "1", "7", "1", "1", "2", "1", "1", "1", "2", "7", "1", "2", "2", "1", "1", "1", "3", "7", "1", "3", "2", "1", "1", "1", "4", "7", "1", "4", "2", "1", "1", "1", "5", "7", "1", "5", "2", "1", "1", "1", "6", "7", "1", "6", "2", "1", "1", "1", "7", "7", "1", "7", "2", "1", "1", "1", "8", "7", "1", "8", "2", "1", "1", "1", "9", "7", "1", "9", "2", "1", "1", "1", "10", "7", "1", "10", "2", "1", "1", "1", "11", "7", "1", "11", "2", "1", "1", "1", "12", "7", "1", "12", "2", "1" ]
[ "nonn", "cofr", "easy" ]
29
1
3
[ "A006085", "A019741" ]
[ "M1822" ]
N. J. A. Sloane
2016-05-17T04:04:23
oeisdata/seq/A006/A006085.seq
c29a9f804517d662eefb3d6023207309
A006086
Unitary harmonic numbers (those for which the unitary harmonic mean is an integer).
[ "1", "6", "45", "60", "90", "420", "630", "1512", "3780", "5460", "7560", "8190", "9100", "15925", "16632", "27300", "31500", "40950", "46494", "51408", "55125", "64260", "66528", "81900", "87360", "95550", "143640", "163800", "172900", "185976", "232470", "257040", "330750", "332640", "464940", "565488", "598500", "646425", "661500" ]
[ "nonn", "nice" ]
53
1
2
[ "A006086", "A006087", "A103339", "A103340" ]
[ "M4248" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006086.seq
b6d0318754bbd6b60d2b974365721db3
A006087
Unitary harmonic means H(n) of the unitary harmonic numbers (A006086).
[ "1", "2", "3", "4", "4", "7", "7", "6", "9", "13", "10", "13", "10", "7", "11", "15", "10", "15", "9", "12", "7", "17", "12", "18", "16", "14", "19", "20", "19", "12", "15", "20", "10", "20", "18", "22", "19", "13", "12", "13", "17", "29", "18", "33", "20", "23", "29", "34", "23", "22", "31", "38", "24", "23", "38", "33", "37", "40", "19", "38", "24", "37", "29", "40", "22", "34", "24", "33" ]
[ "nonn", "nice" ]
43
1
2
[ "A006086", "A006087", "A034444", "A034448", "A077610" ]
[ "M0452" ]
N. J. A. Sloane
2023-03-10T09:09:55
oeisdata/seq/A006/A006087.seq
c3bbad16cdf2f293f4ba46173bb64345
A006088
a(n) = (2^n + 2) a(n-1) (kissing number of Barnes-Wall lattice in dimension 2^n).
[ "1", "4", "24", "240", "4320", "146880", "9694080", "1260230400", "325139443200", "167121673804800", "171466837323724800", "351507016513635840000", "1440475753672879672320000", "11803258325595576034990080000", "193408190923209108909347450880000" ]
[ "nonn", "easy" ]
46
0
2
[ "A006088", "A028362", "A081845" ]
[ "M3606" ]
N. J. A. Sloane, John Leech
2022-09-08T08:44:34
oeisdata/seq/A006/A006088.seq
3e4dcbb91c0a22eb18f926f11d062356
A006089
Coefficients of elliptic function cn.
[ "16", "912", "30768", "870640", "22945056", "586629984", "14804306080", "371548371744", "9303419165040", "232733558500720", "5819812891661136", "145509858586733712", "3637888729721421568" ]
[ "nonn", "easy" ]
34
2
1
[ "A002753", "A006089" ]
[ "M5026" ]
N. J. A. Sloane
2023-10-20T10:01:16
oeisdata/seq/A006/A006089.seq
587b851722b209eaa34126a1947b343a
A006090
Expansion of bracket function.
[ "1", "-6", "21", "-56", "126", "-252", "463", "-804", "1365", "-2366", "4368", "-8736", "18565", "-40410", "87381", "-184604", "379050", "-758100", "1486675", "-2884776", "5592405", "-10919090", "21572460", "-43144920", "87087001", "-176565486", "357913941", "-723002336" ]
[ "sign" ]
21
0
2
[ "A000748", "A000749", "A000750", "A001659", "A006090", "A307047" ]
null
David Callan
2025-01-05T19:51:33
oeisdata/seq/A006/A006090.seq
eb1a18f3580468705910e1d1bd43bb93
A006091
a(n) = n^n - n + 1.
[ "1", "3", "25", "253", "3121", "46651", "823537", "16777209", "387420481", "9999999991", "285311670601", "8916100448245", "302875106592241", "11112006825558003", "437893890380859361", "18446744073709551601", "827240261886336764161", "39346408075296537575407", "1978419655660313589123961" ]
[ "nonn", "easy", "changed" ]
50
1
2
[ "A006091", "A014293" ]
[ "M3111" ]
N. J. A. Sloane
2025-04-17T01:55:05
oeisdata/seq/A006/A006091.seq
ba3a951095607593da97c50d01402400
A006092
Numbers beginning with letter 't' when spelled out in English.
[ "2", "3", "10", "12", "13", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "200", "201", "202", "203", "204", "205", "206", "207", "208", "209", "210", "211", "212", "213", "214", "215", "216", "217", "218", "219", "220" ]
[ "word", "nonn" ]
31
1
1
null
[ "M0901" ]
N. J. A. Sloane.
2024-12-28T23:15:43
oeisdata/seq/A006/A006092.seq
c0f82dc4219d0668746db6377abe6d1b
A006093
a(n) = prime(n) - 1.
[ "1", "2", "4", "6", "10", "12", "16", "18", "22", "28", "30", "36", "40", "42", "46", "52", "58", "60", "66", "70", "72", "78", "82", "88", "96", "100", "102", "106", "108", "112", "126", "130", "136", "138", "148", "150", "156", "162", "166", "172", "178", "180", "190", "192", "196", "198", "210", "222", "226", "228", "232", "238", "240", "250", "256", "262", "268", "270" ]
[ "nonn", "easy", "nice" ]
243
1
2
[ "A000040", "A005867", "A006093", "A008864", "A034693", "A034694", "A039915", "A050997", "A060800", "A072668", "A072670", "A075728", "A084920", "A086145", "A087738", "A101301", "A124223", "A131424", "A131991", "A131992", "A131993", "A162619", "A174996", "A212157", "A249741", "A352707", "A378979", "A379010" ]
[ "M1006" ]
N. J. A. Sloane
2024-12-29T00:42:53
oeisdata/seq/A006/A006093.seq
fe841d9661283b661d0bfb8a55fb1f18
A006094
Products of 2 successive primes.
[ "6", "15", "35", "77", "143", "221", "323", "437", "667", "899", "1147", "1517", "1763", "2021", "2491", "3127", "3599", "4087", "4757", "5183", "5767", "6557", "7387", "8633", "9797", "10403", "11021", "11663", "12317", "14351", "16637", "17947", "19043", "20711", "22499", "23707", "25591", "27221", "28891", "30967", "32399", "34571", "36863" ]
[ "nonn", "easy", "nice" ]
126
1
1
[ "A000040", "A006094", "A006881", "A030664", "A046301", "A046302", "A046303", "A046324", "A046325", "A046326", "A046327", "A078898", "A090076", "A090090", "A097889", "A152241", "A166329", "A219603", "A256617" ]
[ "M4110" ]
N. J. A. Sloane
2024-10-19T08:32:47
oeisdata/seq/A006/A006094.seq
da985139e991212b24c3913611d2dfcf
A006095
Gaussian binomial coefficient [n,2] for q=2.
[ "0", "0", "1", "7", "35", "155", "651", "2667", "10795", "43435", "174251", "698027", "2794155", "11180715", "44731051", "178940587", "715795115", "2863245995", "11453115051", "45812722347", "183251413675", "733006703275", "2932028910251", "11728119835307", "46912487729835" ]
[ "nonn", "easy", "nice" ]
146
0
4
[ "A000225", "A000392", "A002275", "A002452", "A003462", "A003463", "A003464", "A006095", "A006516", "A016123", "A016125", "A016208", "A016256", "A023000", "A023001", "A075113", "A130324", "A203235" ]
[ "M4415" ]
N. J. A. Sloane
2025-02-11T10:31:23
oeisdata/seq/A006/A006095.seq
3281aad4d24439f2562a2142a15a0854
A006096
Gaussian binomial coefficient [ n,3 ] for q=2.
[ "1", "15", "155", "1395", "11811", "97155", "788035", "6347715", "50955971", "408345795", "3269560515", "26167664835", "209386049731", "1675267338435", "13402854502595", "107225699266755", "857817047249091", "6862582190715075", "54900840777134275", "439207459223777475" ]
[ "nonn", "easy", "nice", "changed" ]
62
3
2
[ "A006096", "A092237" ]
[ "M4982" ]
N. J. A. Sloane
2025-04-24T08:06:56
oeisdata/seq/A006/A006096.seq
a258f470846ab45fa4c3979d6d20c39f
A006097
Gaussian binomial coefficient [ n,4 ] for q=2.
[ "1", "31", "651", "11811", "200787", "3309747", "53743987", "866251507", "13910980083", "222984027123", "3571013994483", "57162391576563", "914807651274739", "14638597687734259", "234230965858250739", "3747802679431278579", "59965700687947706355", "959458073589354016755" ]
[ "nonn", "easy", "nice" ]
51
4
2
null
[ "M5226" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006097.seq
44179e359f8ddcdd4afe3948558e2839
A006098
Gaussian binomial coefficient [ 2n,n ] for q=2.
[ "1", "3", "35", "1395", "200787", "109221651", "230674393235", "1919209135381395", "63379954960524853651", "8339787869494479328087443", "4380990637147598617372537398675", "9196575543360038413217351554014467475", "77184136346814161837268404381760884963259795" ]
[ "nonn" ]
52
0
2
[ "A006098", "A022166", "A065446" ]
[ "M3138" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006098.seq
1d8f4d76b31b933aa111f50e9567e57e
A006099
Gaussian binomial coefficient [ n, n/2 ] for q=2.
[ "1", "1", "3", "7", "35", "155", "1395", "11811", "200787", "3309747", "109221651", "3548836819", "230674393235", "14877590196755", "1919209135381395", "246614610741341843", "63379954960524853651", "16256896431763117598611", "8339787869494479328087443", "4274137206973266943778085267" ]
[ "nonn" ]
28
0
3
[ "A006099", "A065446" ]
[ "M2700" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006099.seq
973671a943d133295ec6054ae2c82c9a
A006100
Gaussian binomial coefficient [ n,2 ] for q=3.
[ "1", "13", "130", "1210", "11011", "99463", "896260", "8069620", "72636421", "653757313", "5883904390", "52955405230", "476599444231", "4289397389563", "38604583680520", "347441274648040", "3126971536402441" ]
[ "nonn" ]
43
2
2
[ "A006100", "A203243" ]
[ "M4912" ]
N. J. A. Sloane
2022-04-13T13:25:18
oeisdata/seq/A006/A006100.seq
85c46027f68fc9635dd4a3277b634b91