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1999-12-11 03:00:00
2025-04-28 00:58:08
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A006301
Number of rooted genus-2 maps with n edges.
[ "0", "0", "0", "0", "21", "966", "27954", "650076", "13271982", "248371380", "4366441128", "73231116024", "1183803697278", "18579191525700", "284601154513452", "4272100949982600", "63034617139799916", "916440476048146056", "13154166812674577412", "186700695099591735024", "2623742783421329300190", "36548087103760045010148", "505099724454854883618924" ]
[ "nonn" ]
39
0
5
[ "A000168", "A006300", "A006301", "A104742", "A215402", "A238355", "A238356", "A238357", "A238358", "A238359", "A238360", "A238396" ]
[ "M5120" ]
N. J. A. Sloane and Simon Plouffe
2024-08-23T03:16:57
oeisdata/seq/A006/A006301.seq
4d700a6c9156a074e2f16a5282bccbb7
A006302
Related to enumeration of rooted maps.
[ "4", "28", "148", "704", "3176" ]
[ "nonn", "more" ]
13
2
1
[ "A006302", "A006303" ]
[ "M3622" ]
N. J. A. Sloane.
2021-05-09T06:07:28
oeisdata/seq/A006/A006302.seq
69486e0ab5079145d8b1acf3b71bd90c
A006303
Related to enumeration of rooted maps.
[ "1", "37", "530", "5245", "42406" ]
[ "nonn", "more" ]
11
2
2
[ "A006302", "A006303" ]
[ "M5263" ]
N. J. A. Sloane.
2021-05-09T06:07:35
oeisdata/seq/A006/A006303.seq
0f89d48b972f623f40da7e285e48b6c1
A006304
Coefficients of the '2nd-order' mock theta function A(q).
[ "0", "1", "2", "3", "5", "8", "11", "16", "23", "31", "43", "58", "76", "101", "132", "170", "219", "280", "354", "447", "562", "699", "869", "1076", "1323", "1625", "1987", "2418", "2937", "3556", "4289", "5162", "6196", "7413", "8853", "10547", "12530", "14860", "17586", "20763", "24474", "28792", "33802", "39624", "46368", "54163" ]
[ "nonn", "easy", "nice" ]
31
0
3
[ "A006304", "A006305", "A006306" ]
[ "M0685" ]
N. J. A. Sloane
2021-12-18T23:39:43
oeisdata/seq/A006/A006304.seq
0da342af49e6339c9ecd43ee63856a4c
A006305
Taylor series related to one in Ramanujan's Lost Notebook.
[ "1", "2", "4", "6", "10", "16", "25", "38", "58", "84", "122", "174", "244", "338", "465", "630", "850", "1136", "1508", "1988", "2608", "3398", "4408", "5688", "7306", "9342", "11900", "15090", "19070", "24008", "30122", "37666", "46955", "58348", "72302", "89338", "110094", "135316", "165912", "202924", "247632", "301508" ]
[ "nonn", "easy", "nice" ]
28
0
2
[ "A006304", "A006305", "A006306" ]
[ "M1014" ]
N. J. A. Sloane
2021-12-18T22:17:12
oeisdata/seq/A006/A006305.seq
1989d3239e7f76080baf65912c00b7a8
A006306
Coefficients of the '2nd-order' mock theta function mu(q).
[ "1", "-1", "1", "2", "-1", "-4", "1", "5", "-2", "-5", "4", "7", "-4", "-11", "3", "13", "-6", "-14", "9", "18", "-7", "-24", "8", "29", "-14", "-32", "17", "38", "-18", "-50", "20", "58", "-25", "-63", "33", "77", "-35", "-94", "36", "108", "-48", "-122", "60", "141", "-63", "-170", "70", "195", "-87", "-215", "101", "250", "-110", "-294", "124", "333", "-146", "-371", "173", "424", "-190", "-492", "206", "554", "-245", "-617", "283" ]
[ "sign", "easy", "nice" ]
26
0
4
[ "A006304", "A006305", "A006306" ]
[ "M0163" ]
N. J. A. Sloane
2021-12-18T22:17:03
oeisdata/seq/A006/A006306.seq
e0501f6a8c452a3cf74746085167ca32
A006307
Number of ways writing 2^n as unordered sums of 2 primes.
[ "0", "0", "1", "1", "2", "2", "5", "3", "8", "11", "22", "25", "53", "76", "151", "244", "435", "749", "1314", "2367", "4239", "7471", "13705", "24928", "45746", "83467", "153850", "283746", "525236", "975685", "1817111", "3390038", "6341424", "11891654", "22336060", "42034097", "79287664", "149711134", "283277225", "536710100", "1018369893" ]
[ "nonn" ]
29
0
5
[ "A006307", "A061358", "A062602", "A062610" ]
[ "M0344" ]
N. J. A. Sloane
2021-12-26T21:32:37
oeisdata/seq/A006/A006307.seq
8808cb8584fca802fa27183aa410a834
A006308
Coefficients of period polynomials.
[ "3", "10", "21", "55", "78", "136", "171", "253", "406", "465", "666", "820", "903", "1081", "1378", "1711", "1830", "2211", "2485", "2628", "3081", "3403", "3916", "4656", "5050" ]
[ "nonn" ]
18
2
1
[ "A006308", "A008837" ]
[ "M2834" ]
N. J. A. Sloane.
2020-02-17T11:58:33
oeisdata/seq/A006/A006308.seq
6e038a67260c66452fa2734fc34455bc
A006309
Coefficients of period polynomials.
[ "1", "5", "-21", "33", "-65", "85", "-133", "161", "261", "-341", "-481", "533", "-645", "705", "901", "-12803", "-1281", "-1541", "1633", "-1825", "-14615", "-11537", "2581", "-3201", "3333" ]
[ "sign", "more" ]
21
2
2
null
[ "M3912" ]
N. J. A. Sloane.
2024-03-25T12:06:07
oeisdata/seq/A006/A006309.seq
e4ffaccfef56dc1453ba6720936a60a2
A006310
a(n) = norm of Heilbronn sum NH_{p}, with p = prime(n).
[ "-1", "-1", "97", "-243", "12167", "577", "221874931", "157112485811", "-2480435158303", "310695313260929", "-51140551819476687829", "2727257042363914863401", "-2572343484535669027372727", "1052824394331287344099620777449" ]
[ "sign" ]
26
1
3
null
[ "M5366" ]
N. J. A. Sloane
2017-03-06T03:30:26
oeisdata/seq/A006/A006310.seq
3963bb7d7d44531bee0d8844bb2fb2a7
A006311
Coefficients of period polynomials.
[ "-3", "10", "-84", "-10989", "363883", "-82620", "-137550709", "645413252986", "-7142036935967", "-7522164033404415", "-217498966742521653325", "-10590850429623318361311", "14571491290875996179048369", "-5355885371863393108886638462583" ]
[ "sign" ]
9
2
1
null
[ "M2876" ]
N. J. A. Sloane.
2017-03-08T09:29:23
oeisdata/seq/A006/A006311.seq
1359c2e3f9bf3ba6aac73623cfe31614
A006312
Discriminants of period polynomials.
[ "81", "4375", "69295261", "371972347451121286741113", "43302903550016395864300853167188017879", "25144738658938788754208745610920677061666593988661952539802650899625553" ]
[ "nonn" ]
13
3
1
null
[ "M5357" ]
N. J. A. Sloane.
2017-03-08T09:29:33
oeisdata/seq/A006/A006312.seq
59bb5bfe193e67a2c314d5a9ac6d9889
A006313
Numbers n such that n^16 + 1 is prime.
[ "1", "2", "44", "74", "76", "94", "156", "158", "176", "188", "198", "248", "288", "306", "318", "330", "348", "370", "382", "396", "452", "456", "470", "474", "476", "478", "560", "568", "598", "642", "686", "688", "690", "736", "774", "776", "778", "790", "830", "832", "834", "846", "900", "916", "946", "956", "972", "982", "984", "1018", "1044", "1078" ]
[ "nonn" ]
51
1
2
[ "A000068", "A005574", "A006313", "A006314", "A006315", "A006316", "A056994", "A056995", "A057002", "A057465", "A088361", "A088362", "A226528", "A226529", "A226530", "A243959", "A244150", "A251597", "A253854", "A321323" ]
[ "M2164" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006313.seq
17a8b99c2c326a8dfcd2cdd6fc8bc5c0
A006314
Numbers n such that n^8 + 1 is prime.
[ "1", "2", "4", "118", "132", "140", "152", "208", "240", "242", "288", "290", "306", "378", "392", "426", "434", "442", "508", "510", "540", "542", "562", "596", "610", "664", "680", "682", "732", "782", "800", "808", "866", "876", "884", "892", "916", "918", "934", "956", "990", "1022", "1028", "1054", "1106", "1120", "1174", "1224", "1232", "1256", "1284" ]
[ "nonn", "easy" ]
50
1
2
[ "A000068", "A005574", "A006313", "A006314", "A006315", "A006316", "A056994", "A056995", "A057002", "A057465", "A088361", "A088362", "A226528", "A226529", "A226530", "A243959", "A244150", "A251597", "A253854", "A321323" ]
[ "M1308" ]
N. J. A. Sloane
2024-12-06T04:04:42
oeisdata/seq/A006/A006314.seq
0e83a4cfe5f56e8b586cf120e1c4228d
A006315
Numbers n such that n^32 + 1 is prime.
[ "1", "30", "54", "96", "112", "114", "132", "156", "332", "342", "360", "376", "428", "430", "432", "448", "562", "588", "726", "738", "804", "850", "884", "1068", "1142", "1198", "1306", "1540", "1568", "1596", "1678", "1714", "1754", "1812", "1818", "1878", "1906", "1960", "1962", "2046", "2098", "2118", "2142", "2330", "2418", "2434", "2654", "2668" ]
[ "nonn", "easy" ]
42
1
2
[ "A000068", "A005574", "A006313", "A006314", "A006315", "A006316", "A056994", "A056995", "A057002", "A057465", "A088361", "A088362", "A226528", "A226529", "A226530", "A243959", "A244150", "A251597", "A253854", "A321323" ]
[ "M5208" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006315.seq
d817a88cc0eb8ee7a3f0a7a91e7711e1
A006316
Numbers k such that k^64 + 1 is prime.
[ "1", "102", "162", "274", "300", "412", "562", "592", "728", "1084", "1094", "1108", "1120", "1200", "1558", "1566", "1630", "1804", "1876", "2094", "2162", "2164", "2238", "2336", "2388", "2420", "2494", "2524", "2614", "2784", "3024", "3104", "3140", "3164", "3254", "3278", "3628", "3694", "3738", "3750", "4000", "4030", "4058", "4166" ]
[ "nonn", "easy" ]
56
1
2
[ "A000068", "A005574", "A006313", "A006314", "A006315", "A006316", "A056994", "A056995", "A057002", "A057465", "A088361", "A088362", "A226528", "A226529", "A226530", "A243959", "A244150", "A251597", "A253854", "A321323" ]
[ "M5368" ]
N. J. A. Sloane, Robert G. Wilson v
2022-09-08T08:44:34
oeisdata/seq/A006/A006316.seq
4d51bdcd177f473f742b0dd862dd520a
A006317
Maximum number of chess queens of 3 colors on an n X n board such that no queen attacks or protects another queen of its color.
[ "1", "3", "7", "12", "19", "27", "37", "46", "58", "71", "86", "102", "121", "137", "157", "178", "201", "225", "253", "276", "304", "334", "364" ]
[ "nonn", "more" ]
23
1
2
null
[ "M2631" ]
N. J. A. Sloane
2014-03-30T04:18:01
oeisdata/seq/A006/A006317.seq
c4bccc20b3dd80f1235229212c6bf337
A006318
Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers).
[ "1", "2", "6", "22", "90", "394", "1806", "8558", "41586", "206098", "1037718", "5293446", "27297738", "142078746", "745387038", "3937603038", "20927156706", "111818026018", "600318853926", "3236724317174", "17518619320890", "95149655201962", "518431875418926", "2832923350929742", "15521467648875090" ]
[ "nonn", "easy", "core", "nice", "changed" ]
780
0
2
[ "A001003", "A002003", "A004148", "A006318", "A025240", "A027307", "A033877", "A034015", "A060693", "A085403", "A086456", "A088617", "A103137", "A104219", "A112478", "A138462", "A138463", "A144097", "A144156", "A175124", "A243675", "A243676", "A260332" ]
[ "M1659" ]
N. J. A. Sloane
2025-04-18T13:01:14
oeisdata/seq/A006/A006318.seq
f5cf58a8c4869df6d7fb46d560aa7cdc
A006319
Royal paths in a lattice (convolution of A006318).
[ "1", "1", "4", "16", "68", "304", "1412", "6752", "33028", "164512", "831620", "4255728", "22004292", "114781008", "603308292", "3192216000", "16989553668", "90890869312", "488500827908", "2636405463248", "14281895003716", "77631035881072", "423282220216964", "2314491475510816", "12688544297945348" ]
[ "nonn", "easy" ]
116
0
3
[ "A006318", "A006319", "A033877" ]
[ "M3521" ]
N. J. A. Sloane
2024-07-31T09:07:49
oeisdata/seq/A006/A006319.seq
3c7c754d9d3eebabe91c712300f7d580
A006320
Royal paths in a lattice.
[ "1", "6", "30", "146", "714", "3534", "17718", "89898", "461010", "2386390", "12455118", "65478978", "346448538", "1843520670", "9859734630", "52974158938", "285791932578", "1547585781414", "8408765223294", "45830521556466", "250501529133930", "1372777379874926", "7541129471504790", "41518462993275786" ]
[ "nonn" ]
40
0
2
[ "A006318", "A006320", "A033877" ]
[ "M4200" ]
N. J. A. Sloane
2024-11-26T08:32:30
oeisdata/seq/A006/A006320.seq
0639550d028a8bb7b0ec57deee914172
A006321
Royal paths in a lattice.
[ "1", "8", "48", "264", "1408", "7432", "39152", "206600", "1093760", "5813000", "31019568", "166188552", "893763840", "4823997960", "26124870640", "141926904328", "773293020928", "4224773978632", "23139861329456", "127039971696392", "698993630524032", "3853860616119048", "21288789223825648" ]
[ "nonn" ]
32
0
2
[ "A006321", "A033877" ]
[ "M4535" ]
N. J. A. Sloane
2017-11-06T02:41:16
oeisdata/seq/A006/A006321.seq
a852bce361e6911a5a51eb0c3defc7ef
A006322
4-dimensional analog of centered polygonal numbers.
[ "1", "8", "31", "85", "190", "371", "658", "1086", "1695", "2530", "3641", "5083", "6916", "9205", "12020", "15436", "19533", "24396", "30115", "36785", "44506", "53383", "63526", "75050", "88075", "102726", "119133", "137431", "157760", "180265", "205096", "232408", "262361", "295120", "330855" ]
[ "nonn", "easy" ]
92
1
2
[ "A000217", "A000330", "A006322", "A006414", "A050446", "A050447" ]
null
Albert Rich (AlbertRich(AT)msn.com)
2022-05-28T08:07:21
oeisdata/seq/A006/A006322.seq
19a17b863542ad663ca1ee72fe670a03
A006323
4-dimensional analog of centered polygonal numbers.
[ "1", "10", "41", "115", "260", "511", "910", "1506", "2355", "3520", "5071", "7085", "9646", "12845", "16780", "21556", "27285", "34086", "42085", "51415", "62216", "74635", "88826", "104950", "123175", "143676", "166635", "192241", "220690", "252185", "286936", "325160", "367081", "412930" ]
[ "nonn", "easy" ]
24
1
2
null
null
Albert Rich (AlbertRich(AT)msn.com)
2022-12-27T16:29:42
oeisdata/seq/A006/A006323.seq
102c8c4948adf9452241fe34ebd479ea
A006324
a(n) = n*(n + 1)*(2*n^2 + 2*n - 1)/6.
[ "1", "11", "46", "130", "295", "581", "1036", "1716", "2685", "4015", "5786", "8086", "11011", "14665", "19160", "24616", "31161", "38931", "48070", "58730", "71071", "85261", "101476", "119900", "140725", "164151", "190386", "219646", "252155", "288145", "327856", "371536", "419441", "471835", "528990", "591186" ]
[ "nonn", "easy" ]
57
1
2
[ "A000217", "A000447", "A000539", "A002415", "A006324", "A053134", "A162011", "A162012", "A162013" ]
null
Albert Rich (AlbertRich(AT)msn.com), Jun 14 1998
2024-02-13T20:04:49
oeisdata/seq/A006/A006324.seq
a0a148c0215cba89e81fe463d2f7de8d
A006325
4-dimensional analog of centered polygonal numbers.
[ "0", "0", "1", "7", "26", "70", "155", "301", "532", "876", "1365", "2035", "2926", "4082", "5551", "7385", "9640", "12376", "15657", "19551", "24130", "29470", "35651", "42757", "50876", "60100", "70525", "82251", "95382", "110026", "126295", "144305", "164176", "186032", "210001", "236215", "264810", "295926" ]
[ "nonn", "easy" ]
120
0
4
[ "A000027", "A000217", "A005900", "A006325", "A019298", "A061907", "A169938", "A213751", "A244497", "A244873", "A244879", "A244880", "A288486", "A293309", "A293310", "A293311", "A293312" ]
null
Albert Rich (AlbertRich(AT)msn.com)
2024-09-29T04:32:43
oeisdata/seq/A006/A006325.seq
5ef9c05d301fc207fbe607ad54ac1301
A006326
Total preorders.
[ "1", "5", "24", "122", "680", "4155", "27776", "202084", "1592064", "13513825", "123025408", "1196165886", "12374422528", "135740585015", "1573990072320", "19239037403528", "247255523459072", "3333340694137725", "47039231504678912", "693488743931379010", "10661950808321949696", "170659875799127955955" ]
[ "nonn" ]
28
3
2
[ "A000111", "A006326", "A079502" ]
[ "M3931" ]
N. J. A. Sloane
2019-06-01T11:30:35
oeisdata/seq/A006/A006326.seq
8d49c10ff06cc24d354bbdd66df0a14d
A006327
a(n) = Fibonacci(n) - 3. Number of total preorders.
[ "0", "2", "5", "10", "18", "31", "52", "86", "141", "230", "374", "607", "984", "1594", "2581", "4178", "6762", "10943", "17708", "28654", "46365", "75022", "121390", "196415", "317808", "514226", "832037", "1346266", "2178306", "3524575", "5702884", "9227462", "14930349", "24157814", "39088166", "63245983", "102334152", "165580138" ]
[ "nonn", "easy", "nice" ]
67
4
2
[ "A000045", "A000071", "A001611", "A001911", "A006327", "A079502", "A157725", "A157726", "A157727", "A157728", "A157729", "A167616" ]
[ "M1371" ]
N. J. A. Sloane, Simon Plouffe
2022-09-08T08:44:34
oeisdata/seq/A006/A006327.seq
7c78f07699d94ad2d50c27ddc167e137
A006328
Total preorders.
[ "5", "24", "79", "223", "579", "1432", "3434", "8071", "18714", "42991", "98127", "222965", "505008", "1141236", "2574845", "5802636", "13065935", "29403439", "66141015", "148734156", "334391354", "751675943", "1689494650", "3797059555", "8533209055", "19176039925", "43091557504", "96831330948", "217586892705" ]
[ "nonn", "easy" ]
21
3
1
[ "A006328", "A079502" ]
[ "M3928" ]
N. J. A. Sloane
2017-11-07T18:15:42
oeisdata/seq/A006/A006328.seq
a952503dbd45a760bb65d4ad979bb2ad
A006329
Total preorders.
[ "1", "10", "79", "602", "4682", "38072", "326570", "2964992", "28506383", "289973248", "3116028865", "35308153600", "421048783264", "5273818620928", "69250997724484", "951571372015616", "13658940616055885", "204474999700324352", "3187421031909630947", "51663403849575956480" ]
[ "nonn" ]
22
3
2
[ "A006329", "A079502" ]
[ "M4728" ]
N. J. A. Sloane
2017-11-07T18:15:49
oeisdata/seq/A006/A006329.seq
f648c5a9bdbad166673945bad07a1036
A006330
Number of corners, or planar partitions of n with only one row and one column.
[ "1", "1", "3", "6", "12", "21", "38", "63", "106", "170", "272", "422", "653", "986", "1482", "2191", "3218", "4666", "6726", "9592", "13602", "19122", "26733", "37102", "51232", "70292", "95989", "130356", "176246", "237120", "317724", "423840", "563266", "745562", "983384", "1292333", "1692790", "2209886", "2876132" ]
[ "nonn" ]
56
0
3
[ "A000219", "A000712", "A006330", "A197870", "A247255", "A259100" ]
[ "M2553" ]
N. J. A. Sloane
2017-11-07T18:15:58
oeisdata/seq/A006/A006330.seq
1ca8fd33644e26ebb6155858e2484906
A006331
a(n) = n*(n+1)*(2*n+1)/3.
[ "0", "2", "10", "28", "60", "110", "182", "280", "408", "570", "770", "1012", "1300", "1638", "2030", "2480", "2992", "3570", "4218", "4940", "5740", "6622", "7590", "8648", "9800", "11050", "12402", "13860", "15428", "17110", "18910", "20832", "22880", "25058", "27370", "29820", "32412", "35150", "38038", "41080", "44280" ]
[ "nonn", "easy", "nice" ]
200
0
2
[ "A002378", "A005900", "A006331", "A028896", "A035597", "A046092", "A048147", "A077415", "A084980", "A096000", "A098077", "A100178", "A112524", "A132339", "A163102", "A188475" ]
[ "M1963" ]
N. J. A. Sloane
2024-08-02T22:38:12
oeisdata/seq/A006/A006331.seq
57bd97173a88014cbf472da2652797e2
A006332
From the enumeration of corners.
[ "0", "2", "28", "168", "660", "2002", "5096", "11424", "23256", "43890", "77924", "131560", "212940", "332514", "503440", "742016", "1068144", "1505826", "2083692", "2835560", "3801028", "5026098", "6563832", "8475040", "10829000", "13704210", "17189172", "21383208", "26397308", "32355010", "39393312", "47663616", "57332704" ]
[ "nonn", "easy" ]
48
0
2
[ "A006332", "A006858", "A132339" ]
[ "M2148" ]
N. J. A. Sloane
2024-08-02T22:38:23
oeisdata/seq/A006/A006332.seq
077b00e4fa44cfe0bc58ca7497ee053f
A006333
From the enumeration of corners.
[ "0", "2", "60", "660", "4290", "20020", "74256", "232560", "639540", "1586310", "3617900", "7696260", "15438150", "29451240", "53796160", "94607040", "160908264", "265670730", "427156860", "670609940", "1030350090", "1552346268", "2297341200", "3344614000", "4796473500" ]
[ "nonn", "easy" ]
31
0
2
[ "A006333", "A132339" ]
[ "M2175" ]
N. J. A. Sloane
2024-08-02T22:38:29
oeisdata/seq/A006/A006333.seq
8fa1e64723df5db3e1b707a29cc679b8
A006334
From the enumeration of corners.
[ "0", "2", "110", "2002", "20020", "136136", "705432", "2984520", "10786908", "34370050", "98768670", "260390130", "638110200", "1468635168", "3200871520", "6650874912", "13248113736", "25415833170", "47143878782", "84832157410", "148507792972", "253549890440", "423093671000", "691331713800", "1107985378500" ]
[ "nonn", "easy" ]
32
0
2
[ "A006334", "A132339" ]
[ "M2179" ]
N. J. A. Sloane
2024-08-02T22:38:39
oeisdata/seq/A006/A006334.seq
02cb6c4d4e3785ece4f2a62ea7a38b8d
A006335
a(n) = 4^n*(3*n)!/((n+1)!*(2*n+1)!).
[ "1", "2", "16", "192", "2816", "46592", "835584", "15876096", "315031552", "6466437120", "136383037440", "2941129850880", "64614360416256", "1442028424527872", "32619677465182208", "746569714888605696", "17262927525017812992", "402801642250415636480", "9474719710174783733760", "224477974671833337692160" ]
[ "nonn", "easy" ]
80
0
2
[ "A000309", "A006335", "A098272", "A098273", "A176129", "A214631", "A214722", "A340591" ]
[ "M2094" ]
N. J. A. Sloane
2025-01-07T13:34:23
oeisdata/seq/A006/A006335.seq
f07ea2af891ae8da6b6760b47a4bdbb0
A006336
a(n) = a(n-1) + a(n - 1 - number of even terms so far).
[ "1", "2", "3", "5", "8", "11", "16", "21", "29", "40", "51", "67", "88", "109", "138", "167", "207", "258", "309", "376", "443", "531", "640", "749", "887", "1054", "1221", "1428", "1635", "1893", "2202", "2511", "2887", "3330", "3773", "4304", "4835", "5475", "6224", "6973", "7860", "8747", "9801", "11022", "12243", "13671", "15306", "16941" ]
[ "nonn", "easy", "nice" ]
53
1
2
[ "A000123", "A001950", "A005704", "A006336", "A007604", "A060144", "A131882", "A134408", "A134409" ]
[ "M0684" ]
D. R. Hofstadter, Jul 15 1977
2023-10-29T21:16:42
oeisdata/seq/A006/A006336.seq
53380123863b9c30b62035b1ee79384b
A006337
An "eta-sequence": a(n) = floor( (n+1)*sqrt(2) ) - floor( n*sqrt(2) ).
[ "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1" ]
[ "nonn", "easy", "nice" ]
91
1
2
[ "A001951", "A001952", "A003151", "A003152", "A004641", "A006337", "A006338", "A049472", "A080763", "A082844", "A097509", "A159684", "A188037", "A245219", "A245222", "A276862" ]
[ "M0086" ]
D. R. Hofstadter, Jul 15 1977
2025-02-08T13:06:34
oeisdata/seq/A006/A006337.seq
f1f930dceb44a0456d4ad55a63a00462
A006338
An "eta-sequence": floor((n+1)*sqrt(2) + 1/2) - floor(n*sqrt(2) + 1/2).
[ "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "2" ]
[ "nonn", "easy", "nice" ]
33
1
1
[ "A006337", "A006338", "A022846", "A214848" ]
[ "M0087" ]
D. R. Hofstadter, Jul 15 1977
2022-09-08T08:44:34
oeisdata/seq/A006/A006338.seq
386d5a71fb7274af71c034d23b9e8863
A006339
Least hypotenuse of n distinct Pythagorean triangles.
[ "1", "5", "25", "125", "65", "3125", "15625", "325", "390625", "1953125", "1625", "48828125", "4225", "1105", "6103515625", "30517578125", "40625", "21125", "3814697265625", "203125", "95367431640625", "476837158203125", "5525", "11920928955078125", "274625", "5078125", "1490116119384765625", "528125", "25390625", "186264514923095703125" ]
[ "nonn" ]
31
0
2
[ "A006339", "A046112" ]
null
David W. Wilson
2025-02-16T08:32:30
oeisdata/seq/A006/A006339.seq
4818cb887e014a149e19bd92bcbbe551
A006340
An "eta-sequence": [ (n+1)*tau + 1/2 ] - [ n*tau + 1/2 ], tau = (1 + sqrt(5))/2.
[ "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1" ]
[ "nonn", "easy", "nice" ]
49
0
1
[ "A006340", "A014675", "A245216" ]
[ "M0100" ]
D. R. Hofstadter, Jul 15 1977
2018-08-26T04:45:57
oeisdata/seq/A006/A006340.seq
29b56b7a567cc1680dcfb8756348c7cb
A006341
Octal palindromes which are also primes.
[ "2", "3", "5", "7", "111", "131", "141", "161", "323", "343", "373", "535", "565", "717", "737", "747", "767", "10301", "10601", "11511", "12421", "12621", "13031", "13331", "15151", "16561", "17471", "30403", "30503", "30703", "31313", "31713", "32023", "32323", "33433", "34343", "34443", "35053", "35353", "36463", "36563", "36763", "37473" ]
[ "base", "nonn" ]
12
1
1
[ "A006341", "A029976" ]
null
James Carlson (carlson(AT)xylogics.com)
2025-02-16T08:32:30
oeisdata/seq/A006/A006341.seq
9df6d4f5ec406877d68512bdef131675
A006342
Coloring a circuit with 4 colors.
[ "1", "1", "4", "10", "31", "91", "274", "820", "2461", "7381", "22144", "66430", "199291", "597871", "1793614", "5380840", "16142521", "48427561", "145282684", "435848050", "1307544151", "3922632451", "11767897354", "35303692060", "105911076181", "317733228541", "953199685624", "2859599056870", "8578797170611" ]
[ "nonn", "easy" ]
84
0
3
[ "A006342", "A214142", "A214167" ]
[ "M3398" ]
N. J. A. Sloane, Simon Plouffe
2024-05-27T15:20:19
oeisdata/seq/A006/A006342.seq
36d84d2b1ad1b59137cc1bafc4611e54
A006343
Arkons: number of elementary maps with n-1 nodes.
[ "1", "0", "1", "1", "4", "10", "34", "112", "398", "1443", "5387", "20482", "79177", "310102", "1228187", "4910413", "19792582", "80343445", "328159601", "1347699906", "5561774999", "23052871229", "95926831442", "400587408251", "1678251696379", "7051768702245", "29710764875014" ]
[ "easy", "nonn", "nice" ]
57
0
5
[ "A000108", "A000934", "A006343", "A007318" ]
[ "M3400" ]
N. J. A. Sloane
2024-12-29T03:40:38
oeisdata/seq/A006/A006343.seq
8c2485d2ef244245420a83783d2517f0
A006344
Number of rooted maps with n edges on Klein bottle.
[ "4", "84", "1340", "19280", "263284", "3486224", "45247084", "579150012", "7338291224", "92272957568", "1153361204996", "14348020042512", "177803262186064", "2196338193610064", "27057921450352204", "332583930387073712" ]
[ "nonn" ]
11
2
1
[ "A006344", "A267180" ]
null
Jean-Francois Beraud (beraud(AT)univ-mlv.fr)
2017-09-16T17:10:34
oeisdata/seq/A006/A006344.seq
093ce16f8fe336dc3482833fd7d8c557
A006345
Linus sequence: a(n) "breaks the pattern" by avoiding the longest doubled suffix.
[ "1", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "1", "1", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "1", "1", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "2", "2", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "2", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "2", "2", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "2", "2", "1", "2" ]
[ "nonn", "easy", "nice" ]
125
1
2
[ "A006345", "A006346", "A094840", "A157238" ]
[ "M0074" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006345.seq
24a406db9df8226c9a05dd9e6bcaab9f
A006346
The Sally sequence: the length of repetition avoided in A006345.
[ "0", "1", "1", "2", "1", "3", "1", "1", "3", "2", "1", "6", "3", "2", "1", "3", "1", "1", "6", "3", "2", "4", "1", "1", "3", "2", "1", "3", "1", "6", "4", "2", "1", "2", "4", "3", "1", "8", "3", "2", "1", "6", "3", "2", "1", "3", "1", "1", "6", "3", "2", "4", "1", "1", "3", "2", "1", "3", "1", "30", "6", "3", "2", "4", "1", "1", "3", "2", "1", "3", "1", "6", "4", "2", "1", "2", "4", "3", "1", "8", "3", "2", "1", "6", "3", "2", "1", "3", "1", "1", "6", "3", "2", "4", "1", "1", "3", "2", "1", "3", "1", "6", "4", "2" ]
[ "nonn", "nice", "easy", "look" ]
53
1
4
[ "A006345", "A006346" ]
[ "M0126" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006346.seq
3f9a6238fc8276ffacf07fbb4b4d27c0
A006347
a(n) = (n+1) a(n-1) + (-1)^n.
[ "0", "1", "3", "16", "95", "666", "5327", "47944", "479439", "5273830", "63285959", "822717468", "11518044551", "172770668266", "2764330692255", "46993621768336", "845885191830047", "16071818644770894", "321436372895417879", "6750163830803775460" ]
[ "nonn", "easy" ]
43
1
3
[ "A000166", "A006347" ]
[ "M3018" ]
N. J. A. Sloane
2017-11-07T18:16:26
oeisdata/seq/A006/A006347.seq
358cd648f55c63882e0c126b50a182d9
A006348
a(n) = (n+2)*a(n-1) + (-1)^n.
[ "0", "1", "4", "25", "174", "1393", "12536", "125361", "1378970", "16547641", "215119332", "3011670649", "45175059734", "722800955745", "12287616247664", "221177092457953", "4202364756701106", "84047295134022121", "1764993197814464540", "38829850351918219881", "893086558094119057262" ]
[ "nonn", "easy" ]
33
1
3
null
[ "M3609" ]
N. J. A. Sloane
2017-11-07T05:25:31
oeisdata/seq/A006/A006348.seq
944f3909ed3494f8072cdecc885f3048
A006349
Related to series-parallel networks.
[ "1", "5", "13", "45", "121", "413", "1261", "4221", "13801", "46365", "155497", "527613", "1792805", "6126293", "20986153", "72121853", "248396793", "857416949", "2964896877", "10269596445", "35622421561", "123728022269", "430254861945", "1497796774077", "5219231003621" ]
[ "nonn" ]
8
1
2
[ "A000084", "A000669", "A006349", "A006350", "A058351", "A058352", "A058353" ]
[ "M3834" ]
N. J. A. Sloane.
2012-03-30T16:44:57
oeisdata/seq/A006/A006349.seq
57be9a97ee54e52d0301728c638f9cbe
A006350
Related to series-parallel networks.
[ "0", "1", "7", "27", "101", "337", "1151", "3843", "12965", "43773", "148529", "505605", "1727771", "5920823", "20345445", "70073901", "241849929", "836230109", "2896104951", "10044664507", "34884102385", "121293088909", "422196245641", "1471030361069", "5130057477187", "17905427995239" ]
[ "nonn", "easy" ]
8
1
3
[ "A000084", "A000669", "A006349", "A006350", "A058351", "A058352", "A058353" ]
[ "M4388" ]
N. J. A. Sloane.
2012-03-30T16:44:57
oeisdata/seq/A006/A006350.seq
269dda8b83618c612594134bd8c3df57
A006351
Number of series-parallel networks with n labeled edges. Also called yoke-chains by Cayley and MacMahon.
[ "1", "2", "8", "52", "472", "5504", "78416", "1320064", "25637824", "564275648", "13879795712", "377332365568", "11234698041088", "363581406419456", "12707452084972544", "477027941930515456", "19142041172838025216", "817675811320888020992", "37044610820729973813248", "1774189422608238694776832" ]
[ "nonn", "easy", "nice" ]
165
1
2
[ "A000084", "A000311", "A006351", "A032188", "A133314", "A134991", "A135494", "A140945" ]
[ "M1885" ]
N. J. A. Sloane
2025-01-16T12:38:16
oeisdata/seq/A006/A006351.seq
c3f7423cffde50f59d86efbe0e662d0f
A006352
Coefficients in expansion of Eisenstein series E_2 (also called E_1 or G_2).
[ "1", "-24", "-72", "-96", "-168", "-144", "-288", "-192", "-360", "-312", "-432", "-288", "-672", "-336", "-576", "-576", "-744", "-432", "-936", "-480", "-1008", "-768", "-864", "-576", "-1440", "-744", "-1008", "-960", "-1344", "-720", "-1728", "-768", "-1512", "-1152", "-1296", "-1152", "-2184", "-912", "-1440", "-1344", "-2160", "-1008", "-2304", "-1056", "-2016", "-1872", "-1728" ]
[ "sign", "easy", "nice" ]
75
0
2
[ "A000594", "A004009", "A006352", "A008410", "A013973", "A013974", "A029828", "A029829", "A029830", "A029831", "A058550", "A076835", "A145155" ]
[ "M5145" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006352.seq
0e85f2e7e15c6e7ebc8c6ce7dd10ec68
A006353
Expansion of (phi(-q^3) * psi(q))^3 / (phi(-q) * psi(q^3)) in powers of q where phi(), psi() are Ramanujan theta functions.
[ "1", "5", "13", "23", "29", "30", "31", "40", "61", "77", "78", "60", "47", "70", "104", "138", "125", "90", "85", "100", "174", "184", "156", "120", "79", "155", "182", "239", "232", "150", "186", "160", "253", "276", "234", "240", "101", "190", "260", "322", "366", "210", "248", "220", "348", "462", "312", "240", "143", "285", "403", "414", "406", "270" ]
[ "nonn", "easy", "nice" ]
80
0
2
[ "A000203", "A005259", "A006352", "A006353", "A226235" ]
[ "M3825" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006353.seq
03588b28980ef42f817b90a350343abc
A006354
Expansion of a cusp form of weight 8 for Gamma_1(6).
[ "1", "26", "165", "100", "570", "834", "1664", "856", "2151", "2460", "2316", "9588", "5270", "12160", "24930", "16912", "6498", "4086", "58732", "22440", "150144", "1464", "119112", "121416", "98825", "49604", "334179", "104192", "186018", "388980", "530168", "204704", "147132", "562932", "326400", "111420" ]
[ "nonn" ]
15
1
2
null
[ "M5187" ]
N. J. A. Sloane
2017-11-01T09:17:55
oeisdata/seq/A006/A006354.seq
eba8c048edcf50c2c8d2cd7d76c35953
A006355
Number of binary vectors of length n containing no singletons.
[ "1", "0", "2", "2", "4", "6", "10", "16", "26", "42", "68", "110", "178", "288", "466", "754", "1220", "1974", "3194", "5168", "8362", "13530", "21892", "35422", "57314", "92736", "150050", "242786", "392836", "635622", "1028458", "1664080", "2692538", "4356618", "7049156", "11405774", "18454930", "29860704", "48315634" ]
[ "nonn", "easy", "nice", "changed" ]
195
0
3
[ "A000045", "A006355", "A047992", "A054886", "A055389", "A068922", "A090991", "A094570", "A097925", "A097926", "A118658", "A119457", "A265584" ]
null
David M. Bloom
2025-04-19T10:04:41
oeisdata/seq/A006/A006355.seq
f0f1ed403b31d38ffbc5c4a60ef1d69c
A006356
a(n) = 2*a(n-1) + a(n-2) - a(n-3) for n >= 3, starting with a(0) = 1, a(1) = 3, and a(2) = 6.
[ "1", "3", "6", "14", "31", "70", "157", "353", "793", "1782", "4004", "8997", "20216", "45425", "102069", "229347", "515338", "1157954", "2601899", "5846414", "13136773", "29518061", "66326481", "149034250", "334876920", "752461609", "1690765888", "3799116465", "8536537209", "19181424995" ]
[ "nonn", "easy", "nice", "walk" ]
237
0
2
[ "A000217", "A000330", "A006054", "A006356", "A006357", "A006359", "A025030", "A030112", "A030116", "A033303", "A038196", "A050446", "A050447", "A052534", "A052949", "A052994", "A077998", "A179542", "A180262", "A190360", "A306334" ]
[ "M2578" ]
N. J. A. Sloane
2025-04-12T06:30:44
oeisdata/seq/A006/A006356.seq
8bcca8beec79c20d57e149348d0ae540
A006357
Number of distributive lattices; also number of paths with n turns when light is reflected from 4 glass plates.
[ "1", "4", "10", "30", "85", "246", "707", "2037", "5864", "16886", "48620", "139997", "403104", "1160693", "3342081", "9623140", "27708726", "79784098", "229729153", "661478734", "1904652103", "5484227157", "15791202736", "45468956106", "130922641160", "376976720745", "1085461206128", "3125460977225" ]
[ "nonn", "nice", "easy" ]
75
0
2
[ "A000217", "A000330", "A006356", "A006357", "A006359", "A025030", "A030112", "A030116", "A038197", "A050446", "A050447", "A091024", "A122167" ]
[ "M3396" ]
N. J. A. Sloane
2024-04-20T10:49:00
oeisdata/seq/A006/A006357.seq
2fff41a9a192f5b423a1aea377c7b3e3
A006358
Number of distributive lattices; also number of paths with n turns when light is reflected from 5 glass plates.
[ "1", "5", "15", "55", "190", "671", "2353", "8272", "29056", "102091", "358671", "1260143", "4427294", "15554592", "54648506", "191998646", "674555937", "2369942427", "8326406594", "29253473175", "102777312308", "361091343583", "1268635610806", "4457144547354" ]
[ "nonn", "easy", "nice" ]
75
0
2
[ "A000217", "A000330", "A006356", "A006358", "A006359", "A025030", "A030112", "A030116", "A038201", "A050446", "A050447" ]
[ "M3862" ]
N. J. A. Sloane
2024-04-20T10:48:57
oeisdata/seq/A006/A006358.seq
cbf94cbca919d50cee04dce23433abaf
A006359
Number of distributive lattices; also number of paths with n turns when light is reflected from 6 glass plates.
[ "1", "6", "21", "91", "371", "1547", "6405", "26585", "110254", "457379", "1897214", "7869927", "32645269", "135416457", "561722840", "2330091144", "9665485440", "40093544735", "166312629795", "689883899612", "2861717685450", "11870733787751", "49241167758705", "204258021937291", "847285745315256" ]
[ "nonn", "easy" ]
49
0
2
[ "A000217", "A000330", "A006356", "A006357", "A006358", "A006359", "A025030", "A030112", "A030113", "A030114", "A030115", "A030116", "A050446", "A050447" ]
[ "M4148" ]
N. J. A. Sloane
2024-05-02T14:42:09
oeisdata/seq/A006/A006359.seq
8dbc78478556c8a3a587f33b45b4b1a5
A006360
Antichains (or order ideals) in the poset 2*2*3*n or size of the distributive lattice J(2*2*3*n).
[ "1", "50", "887", "8790", "59542", "307960", "1301610", "4701698", "14975675", "43025762", "113414717", "277904900", "639562508", "1393844960", "2896063220", "5768600412", "11066514565", "20526933442", "36936277875", "64660182026", "110394412610" ]
[ "nonn", "easy" ]
38
0
2
[ "A000217", "A000330", "A000372", "A006356", "A006357", "A006358", "A006359", "A006360", "A006361", "A006362", "A050446", "A050447", "A056932", "A056933", "A056934", "A056935", "A056936", "A056937" ]
[ "M5300" ]
N. J. A. Sloane
2025-01-18T04:13:10
oeisdata/seq/A006/A006360.seq
0095dcba689df2a420cfc897ed690311
A006361
Antichains (or order ideals) in the poset 2*2*4*n or size of the distributive lattice J(2*2*4*n).
[ "1", "105", "3490", "59542", "650644", "5157098", "32046856", "164489084", "723509159", "2801747767", "9748942554", "30967306114", "90930233726", "249319296218", "643622467414", "1575086681342", "3675063064675", "8215220917795" ]
[ "nonn", "easy" ]
38
0
2
[ "A000372", "A006360", "A006361", "A006362", "A056932", "A056933", "A056934", "A056935", "A056936", "A056937" ]
[ "M5370" ]
N. J. A. Sloane
2025-01-18T04:12:55
oeisdata/seq/A006/A006361.seq
e708ce739db93b655ce362dd1e5803df
A006362
Antichains (or order ideals) in the poset 2*2*5*n or size of the distributive lattice J(2*2*5*n).
[ "1", "196", "11196", "307960", "5157098", "60112692", "530962446", "3764727340", "22326282261", "114158490576", "515063238810", "2087929609236", "7714649716552", "26285397502428", "83379798088110", "248202756212336", "697998155989501", "1864955619299196" ]
[ "nonn", "easy" ]
28
0
2
[ "A000372", "A006360", "A006361", "A006362", "A056932", "A056933", "A056934", "A056935", "A056936", "A056937" ]
[ "M5411" ]
N. J. A. Sloane
2025-01-18T04:12:46
oeisdata/seq/A006/A006362.seq
5cbaecef5a6f89f9174f2efc6b6530bf
A006363
Number of antichains (or order ideals) in the poset B_4 X [n]; or size of the distributive lattice J(B_4 X [n]).
[ "1", "168", "7581", "160948", "2068224", "18561984", "127234008", "706987164", "3320153661", "13583619496", "49530070161", "163806121656", "498180781144", "1408758106368", "3737505070344", "9372218674824", "22351423903953", "50960797533096", "111574385244253", "235475590500876", "480631725411720", "951504952784320", "1831615165328400", "3435931869872580" ]
[ "nonn" ]
26
0
2
[ "A002415", "A006363", "A056932" ]
[ "M5408" ]
N. J. A. Sloane
2021-01-22T10:40:14
oeisdata/seq/A006/A006363.seq
2befdebec188ac7e8a37cda356772e8b
A006364
Numbers k with an even number of 1's in binary, ignoring last bit.
[ "0", "1", "6", "7", "10", "11", "12", "13", "18", "19", "20", "21", "24", "25", "30", "31", "34", "35", "36", "37", "40", "41", "46", "47", "48", "49", "54", "55", "58", "59", "60", "61", "66", "67", "68", "69", "72", "73", "78", "79", "80", "81", "86", "87", "90", "91", "92", "93", "96", "97", "102", "103", "106", "107", "108", "109", "114", "115", "116", "117", "120", "121", "126", "127", "130", "131", "132" ]
[ "base", "nonn", "nice", "easy" ]
48
1
3
[ "A000120", "A001969", "A006364", "A011371" ]
[ "M4060" ]
N. J. A. Sloane
2024-09-07T08:53:29
oeisdata/seq/A006/A006364.seq
0175ab52c550cb5959cf5aea2a149ac8
A006365
Number of binary tree partitions.
[ "1", "1", "3", "8", "24", "72", "229", "740", "2460", "8317", "28590", "99556", "350661", "1246998", "4471801", "16153007", "58722226", "214687361", "788855637", "2911701588", "10790952975", "40139185202", "149805575022", "560804604385", "2105273566444", "7923577070408", "29892583708055", "113020768615090", "428190609376563", "1625319129822979", "6180270575440241" ]
[ "nonn" ]
26
0
3
null
null
Don Knuth
2025-01-05T19:51:33
oeisdata/seq/A006/A006365.seq
ed27b1323dbba450566b0cd79050e6be
A006366
Number of cyclically symmetric plane partitions in the n-cube; also number of 2n X 2n half-turn symmetric alternating sign matrices divided by number of n X n alternating sign matrices.
[ "1", "2", "5", "20", "132", "1452", "26741", "826540", "42939620", "3752922788", "552176360205", "136830327773400", "57125602787130000", "40191587143536420000", "47663133295107416936400", "95288872904963020131203520", "321195665986577042490185260608" ]
[ "nonn", "nice", "easy" ]
40
0
2
[ "A003827", "A005130", "A005156", "A005158", "A005160", "A005164", "A006366", "A048601", "A050204" ]
[ "M1529" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006366.seq
54167c2e62495989a9c12962167eab8f
A006367
Number of binary vectors of length n+1 beginning with 0 and containing just 1 singleton.
[ "1", "0", "2", "2", "5", "8", "15", "26", "46", "80", "139", "240", "413", "708", "1210", "2062", "3505", "5944", "10059", "16990", "28646", "48220", "81047", "136032", "228025", "381768", "638450", "1066586", "1780061", "2968040", "4944519", "8230370", "13689118", "22751528", "37786915", "62716752", "104028245" ]
[ "nonn", "easy" ]
83
0
3
[ "A000032", "A000045", "A004798", "A006355", "A006367", "A010049", "A105422", "A139821", "A212804" ]
null
David M. Bloom
2023-05-04T17:33:17
oeisdata/seq/A006/A006367.seq
5d1dd2ac470aa8e5608b51dae970f85e
A006368
The "amusical permutation" of the nonnegative numbers: a(2n)=3n, a(4n+1)=3n+1, a(4n-1)=3n-1.
[ "0", "1", "3", "2", "6", "4", "9", "5", "12", "7", "15", "8", "18", "10", "21", "11", "24", "13", "27", "14", "30", "16", "33", "17", "36", "19", "39", "20", "42", "22", "45", "23", "48", "25", "51", "26", "54", "28", "57", "29", "60", "31", "63", "32", "66", "34", "69", "35", "72", "37", "75", "38", "78", "40", "81", "41", "84", "43", "87", "44", "90", "46", "93", "47", "96", "49", "99", "50", "102", "52", "105", "53" ]
[ "nonn", "nice", "easy" ]
150
0
3
[ "A006368", "A006369", "A028294", "A028393", "A028394", "A028395", "A028396", "A028397", "A047529", "A094328", "A094329", "A178414", "A178415", "A180853", "A180864", "A182205", "A185589", "A185590", "A217218", "A217729", "A223083", "A223088", "A265667" ]
[ "M2249" ]
N. J. A. Sloane and J. H. Conway
2024-12-18T09:21:50
oeisdata/seq/A006/A006368.seq
596a42fa1bf2e83f9b31e3883de6a952
A006369
a(n) = 2*n/3 for n divisible by 3, otherwise a(n) = round(4*n/3). Or, equivalently, a(3*n-2) = 4*n-3, a(3*n-1) = 4*n-1, a(3*n) = 2*n.
[ "0", "1", "3", "2", "5", "7", "4", "9", "11", "6", "13", "15", "8", "17", "19", "10", "21", "23", "12", "25", "27", "14", "29", "31", "16", "33", "35", "18", "37", "39", "20", "41", "43", "22", "45", "47", "24", "49", "51", "26", "53", "55", "28", "57", "59", "30", "61", "63", "32", "65", "67", "34", "69", "71", "36", "73", "75", "38", "77", "79", "40", "81", "83", "42", "85", "87", "44", "89", "91", "46", "93", "95" ]
[ "nonn", "nice", "easy" ]
108
0
3
[ "A006368", "A006369", "A028393", "A028394", "A028395", "A028396", "A028397", "A069196", "A094328", "A094329", "A180853", "A180864", "A182205", "A185589", "A185590", "A217218", "A217729", "A223083", "A223088", "A265667" ]
[ "M2245" ]
N. J. A. Sloane and J. H. Conway
2023-02-08T14:08:03
oeisdata/seq/A006/A006369.seq
e191a59fb3b6759657bbfecd2e53fa8e
A006370
The Collatz or 3x+1 map: a(n) = n/2 if n is even, 3n + 1 if n is odd.
[ "0", "4", "1", "10", "2", "16", "3", "22", "4", "28", "5", "34", "6", "40", "7", "46", "8", "52", "9", "58", "10", "64", "11", "70", "12", "76", "13", "82", "14", "88", "15", "94", "16", "100", "17", "106", "18", "112", "19", "118", "20", "124", "21", "130", "22", "136", "23", "142", "24", "148", "25", "154", "26", "160", "27", "166", "28", "172", "29", "178", "30", "184", "31", "190", "32", "196", "33" ]
[ "nonn", "nice", "easy" ]
237
0
2
[ "A001281", "A005408", "A006370", "A006577", "A016825", "A016945", "A070165", "A082286", "A139391", "A347270" ]
[ "M3198" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006370.seq
57be7b0121fbccad5a74c18e9c6dd30b
A006371
Number of reduced binary quadratic forms of discriminant -n.
[ "1", "1", "1", "1", "1", "2", "2", "2", "1", "2", "3", "2", "2", "2", "3", "3", "2", "3", "4", "2", "1", "4", "5", "4", "2", "2", "4", "4", "3", "4", "5", "4", "1", "4", "7", "3", "3", "4", "5", "6", "3", "4", "6", "2", "2", "6", "8", "6", "3", "3", "5", "6", "3", "6", "8", "4", "2", "6", "10", "4", "2", "6", "5", "7", "5", "4", "8", "4", "3", "8", "10", "8", "3", "2", "7", "6", "4", "8", "10", "6", "1", "8" ]
[ "nonn" ]
19
3
6
[ "A006371", "A006374" ]
[ "M0207" ]
N. J. A. Sloane
2017-03-19T19:49:47
oeisdata/seq/A006/A006371.seq
28e9437bda264bb2fd17e45bca4f6d80
A006372
Numbers of terms in expressions for coefficients of "Lovelock Lagrangians" (or "Gauss-Bonnet forms") in terms of Riemann-Christoffel curvature tensor and two of its contractions (viz., the Ricci curvature tensor and the Riemann curvature scalar) for n-dimensional differentiable manifolds having a general linear connection.
[ "1", "1", "3", "8", "25", "85", "397", "2183", "15129", "122585" ]
[ "nonn", "more" ]
30
0
3
[ "A006372", "A006373", "A045900", "A306892" ]
null
C. C. Briggs (ccb104(AT)vm.cac.psu.edu)
2022-07-19T05:49:49
oeisdata/seq/A006/A006372.seq
3c05b60643278a3ca8f9b5f25c415cc8
A006373
Numbers of terms in expressions for coefficients of Euler-Lagrange tensors in terms of Riemann-Christoffel curvature tensor and two of its contractions (viz., the Ricci curvature tensor and the Riemann curvature scalar) for n-dimensional differentiable manifolds having a general linear connection.
[ "1", "2", "7", "26", "115", "596" ]
[ "nonn", "more" ]
20
0
2
[ "A006372", "A006373", "A030429", "A167551" ]
null
C. C. Briggs (ccb104(AT)vm.cac.psu.edu)
2017-08-30T16:10:25
oeisdata/seq/A006/A006373.seq
2c1c5db1af535d68536644fbf0d1d456
A006374
Number of positive definite reduced binary quadratic forms of discriminant -4*n.
[ "1", "1", "2", "2", "2", "2", "2", "3", "3", "2", "4", "4", "2", "4", "4", "4", "4", "3", "4", "6", "4", "2", "6", "6", "3", "6", "6", "4", "6", "4", "6", "7", "4", "4", "8", "8", "2", "6", "8", "6", "8", "4", "4", "10", "6", "4", "10", "8", "5", "7", "8", "6", "6", "8", "8", "12", "4", "2", "12", "8", "6", "8", "10", "8", "8", "8", "4", "12", "8", "4", "14", "9", "4", "10", "10", "10", "8", "4", "10", "14", "9", "4", "12", "12", "4", "10", "12", "6", "12", "10", "8" ]
[ "nonn", "nice", "easy" ]
25
1
3
[ "A006371", "A006374", "A006375", "A096445", "A096446" ]
[ "M0214" ]
N. J. A. Sloane
2019-04-01T06:26:46
oeisdata/seq/A006/A006374.seq
325a0fa9c62898892a0a4ec64a047f1a
A006375
Number of reduced indefinite binary forms of determinant -n.
[ "2", "1", "1", "3", "2", "1", "1", "2", "4", "2", "1", "2", "2", "1", "2", "5", "2", "2", "1", "3", "2", "1", "1", "3", "6", "2", "2", "2", "2", "2", "1", "3", "2", "2", "2", "7", "3", "1", "2", "4", "2", "2", "1", "2", "4", "1", "1", "4", "6", "3", "2", "3", "2", "2", "2", "3", "2", "2", "1", "4", "2", "1", "3", "8", "2", "2", "1", "3", "2", "2" ]
[ "nonn", "hard", "changed" ]
19
1
1
[ "A006371", "A006374", "A006375" ]
[ "M0080" ]
N. J. A. Sloane.
2025-04-20T03:48:25
oeisdata/seq/A006/A006375.seq
1028b485310070d855b9ef4de96e38af
A006376
Number of indecomposable positive definite ternary quadratic forms of determinant n.
[ "0", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "2", "3", "1", "2", "1", "3", "2", "1", "2", "5", "1", "1", "3", "5", "2", "3", "1", "5", "5", "2", "2", "6", "2", "2", "5", "6", "3", "3", "3", "8", "4", "3" ]
[ "nonn", "nice", "more" ]
15
1
19
[ "A006376", "A006377", "A071136" ]
[ "M0402" ]
N. J. A. Sloane
2021-12-17T11:27:25
oeisdata/seq/A006/A006376.seq
24cdb4ba0f3e145ad5291a8dd2c1f40a
A006377
Determinants of indecomposable indefinite ternary quadratic forms.
[ "8", "28", "32", "56", "64", "68", "72", "92" ]
[ "nonn", "nice" ]
13
1
1
[ "A006377", "A071136" ]
[ "M4501" ]
N. J. A. Sloane
2015-06-14T21:15:40
oeisdata/seq/A006/A006377.seq
ce214a01022d7487634dfec2200a6e04
A006378
Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum.
[ "3", "5", "7", "31", "53", "97", "211", "233", "277", "367", "389", "457", "479", "547", "569", "613", "659", "727", "839", "883", "929", "1021", "1087", "1109", "1223", "1289", "1447", "1559", "1627", "1693", "1783", "1873", "2099", "2213", "2347", "2437", "2459", "2503", "2549", "2593", "2617", "2683", "2729", "2819", "2953", "3023", "3067" ]
[ "nonn", "base", "nice", "easy" ]
63
1
1
[ "A000040", "A003052", "A006378", "A007953", "A047791", "A048521", "A049084", "A062028", "A107740", "A247104" ]
[ "M2427" ]
N. J. A. Sloane
2025-03-11T08:42:52
oeisdata/seq/A006/A006378.seq
2ee97a3573c7373828502f838c604a6e
A006379
Number of noncyclic (finite) simple groups with n conjugacy classes.
[ "0", "0", "0", "0", "1", "1", "1", "1", "3", "2", "2", "3", "0", "4", "3", "1", "2", "2", "0", "1", "2" ]
[ "nonn", "nice", "more" ]
21
1
9
[ "A002319", "A003061", "A006379", "A073043" ]
[ "M2241" ]
N. J. A. Sloane
2021-12-19T00:10:11
oeisdata/seq/A006/A006379.seq
77b98b389672436c5b253719a9152dc0
A006380
Number of equivalence classes of 4 X n binary matrices when one can permute rows, permute columns and complement columns.
[ "1", "3", "8", "19", "41", "81", "153", "273", "468", "774", "1240", "1930", "2933", "4356", "6341", "9064", "12743", "17643", "24093", "32479", "43270", "57019", "74377", "96103", "123089", "156354", "197081", "246622", "306519", "378520", "464614", "567028", "688276", "831169", "998845", "1194793", "1422899", "1687447", "1993182" ]
[ "nonn", "easy" ]
31
0
2
[ "A000601", "A006148", "A006380", "A006383", "A363349" ]
[ "M2735" ]
N. J. A. Sloane
2025-03-07T12:02:15
oeisdata/seq/A006/A006380.seq
26229383310587bafd2d52dd8ec4b791
A006381
Number of n X 3 binary matrices under row and column permutations and column complementations.
[ "1", "1", "4", "7", "19", "32", "68", "114", "210", "336", "562", "862", "1349", "1987", "2950", "4201", "5991", "8278", "11422", "15386", "20660", "27218", "35718", "46158", "59401", "75475", "95494", "119545", "149035", "184118", "226562", "276620", "336470", "406490", "489344", "585572", "698397", "828549", "979896" ]
[ "nonn", "nice", "easy" ]
33
0
3
[ "A000601", "A002727", "A005232", "A006148", "A006380", "A006381", "A006382", "A363349" ]
[ "M3313" ]
N. J. A. Sloane
2025-03-07T11:49:16
oeisdata/seq/A006/A006381.seq
2c6a6c169f2484113230d96ad113d1c0
A006382
Number of n X 4 binary matrices under row and column permutations and column complementations.
[ "1", "1", "5", "11", "41", "101", "301", "757", "1981", "4714", "11133", "24763", "53818", "111941", "226857", "444260", "848620", "1576226", "2862426", "5077454", "8827758", "15043096", "25183794", "41434222", "67108437", "107051463", "168402958", "261384026", "400684767", "606936536" ]
[ "nonn" ]
26
0
3
[ "A002727", "A005232", "A006148", "A006380", "A006381", "A006382", "A363349" ]
[ "M3814" ]
N. J. A. Sloane
2025-03-07T12:00:31
oeisdata/seq/A006/A006382.seq
319bcba040c0bcfad58e18af3c1f3fd2
A006383
Number of equivalence classes of n X n binary matrices when one can permute rows, permute columns and complement columns.
[ "1", "1", "3", "7", "41", "299", "6128", "343656", "67013431", "45770163273", "108577103160005", "886929528971819040", "24943191706060101926577", "2425246700258693990625775794", "820270898724825121532156178527106" ]
[ "nonn", "nice", "easy" ]
33
0
3
[ "A002724", "A005232", "A006381", "A006382", "A006383", "A056204", "A056205", "A363349" ]
[ "M2701" ]
N. J. A. Sloane
2023-05-30T15:51:03
oeisdata/seq/A006/A006383.seq
ae1e4ee3d6a3ce06d5f76a043db25eb2
A006384
Number of sensed planar maps with n edges.
[ "1", "2", "4", "14", "57", "312", "2071", "15030", "117735", "967850", "8268816", "72833730", "658049140", "6074058060", "57106433817", "545532037612", "5284835906037", "51833908183164", "514019531037910", "5147924676612282", "52017438279806634", "529867070532745464" ]
[ "nonn", "nice" ]
54
0
2
[ "A000168", "A006384", "A006385", "A006402", "A006443", "A379430" ]
[ "M1281" ]
N. J. A. Sloane
2025-01-14T21:21:36
oeisdata/seq/A006/A006384.seq
2b4823fab0473979d5d5719e99b5a6ab
A006385
Number of unsensed planar maps with n edges.
[ "1", "2", "4", "14", "52", "248", "1416", "9172", "66366", "518868", "4301350", "37230364", "333058463", "3057319072", "28656583950", "273298352168", "2645186193457", "25931472185976", "257086490694917", "2574370590192556", "26010904915620261" ]
[ "nonn", "nice", "more" ]
44
0
2
[ "A000168", "A006384", "A006385", "A006387", "A006403", "A006443", "A090376", "A214814", "A214815", "A214816", "A277741", "A379439" ]
[ "M1279" ]
N. J. A. Sloane
2025-01-20T20:24:42
oeisdata/seq/A006/A006385.seq
d301e8df4f4c6787490b81fe9f343e46
A006386
Number of sensed genus 1 maps with n edges.
[ "1", "6", "46", "452", "4852", "52972", "587047", "6550808", "73483256", "827801468", "9360123740", "106189359544", "1208328304864", "13787042250528", "157700137398689", "1807893066408464", "20768681225892328", "239037464947999900", "2755989928117365244", "31826208029615881656", "368074022535205870382" ]
[ "nice", "nonn" ]
31
2
2
[ "A006300", "A006384", "A006386", "A006387", "A104595", "A104596", "A215019", "A379438" ]
[ "M4253" ]
N. J. A. Sloane
2025-01-21T21:29:37
oeisdata/seq/A006/A006386.seq
83ef5458c827b6f1476db84f96efbe6e
A006387
Number of unsensed genus 1 maps with n edges.
[ "0", "0", "1", "6", "40", "320", "2946", "29364", "309558", "3365108", "37246245", "416751008", "4696232371", "53186743416", "604690121555", "6896534910612", "78867385697513", "904046279771682", "10384916465797240", "119522063788612992", "1378014272286250059" ]
[ "nonn" ]
36
0
4
[ "A006300", "A006385", "A006386", "A006387", "A214814", "A214815", "A214816", "A379439" ]
[ "M4237" ]
N. J. A. Sloane
2025-01-21T21:29:28
oeisdata/seq/A006/A006387.seq
dcc2a7c5868f01895ae7664ea85ffe95
A006388
Number of sensed planar maps with n edges and without faces of degree 1.
[ "1", "1", "2", "6", "18", "74", "393", "2282", "14700", "99614", "703519", "5123598", "38279496" ]
[ "nonn", "more" ]
19
0
3
[ "A006384", "A006388", "A006389", "A379433" ]
[ "M1633" ]
N. J. A. Sloane
2025-01-16T14:17:21
oeisdata/seq/A006/A006388.seq
75c572cdc0b3083e5e34fe1e639474b6
A006389
Number of unsensed planar maps with n edges and without faces of degree 1.
[ "1", "1", "2", "6", "18", "68", "313", "1592", "9187", "57451", "384450", "2703970", "19769311" ]
[ "nonn", "more" ]
19
0
3
[ "A006385", "A006388", "A006389", "A379433" ]
[ "M1632" ]
N. J. A. Sloane
2025-01-16T14:17:24
oeisdata/seq/A006/A006389.seq
c07effa5cbec2c2ce059f574c06f9e6a
A006390
Number of sensed loopless planar maps with n edges.
[ "1", "1", "2", "5", "14", "49", "240", "1259", "7570", "47996", "319518", "2199295", "15571610", "112773478", "832809504", "6253673323", "47650870538", "367784975116", "2871331929096", "22647192990256", "180277915464664", "1447060793168493", "11703567787559680", "95312765368320637", "781151020141584190" ]
[ "nonn" ]
38
0
3
[ "A000010", "A000260", "A006384", "A006390", "A006391", "A103941", "A103942" ]
[ "M1468" ]
N. J. A. Sloane
2025-01-16T11:30:44
oeisdata/seq/A006/A006390.seq
500b8aebd15779c7b7791d7a7c3c2e0b
A006391
Number of unsensed loopless planar maps with n edges.
[ "1", "1", "2", "5", "14", "45", "191", "871", "4682", "27336", "172706", "1150322", "7989004" ]
[ "nonn" ]
19
0
3
[ "A000260", "A006385", "A006390", "A006391" ]
[ "M1464" ]
N. J. A. Sloane
2025-01-16T11:30:40
oeisdata/seq/A006/A006391.seq
035a24c6b51f342e973e0bf71969b2a1
A006392
Number of sensed planar maps with n edges and without faces of degree 1 or 2.
[ "1", "0", "1", "4", "9", "34", "161", "830", "4779", "29092", "184510", "1208178", "8116922" ]
[ "nonn", "more" ]
19
0
4
[ "A006384", "A006388", "A006392", "A006393", "A379434" ]
[ "M3368" ]
N. J. A. Sloane
2025-01-16T14:17:27
oeisdata/seq/A006/A006392.seq
09c43504626fced74d353f866cbf41cf
A006393
Number of unsensed planar maps with n edges and without faces of degree 1 or 2.
[ "1", "0", "1", "4", "9", "32", "132", "597", "3064", "17114", "102274", "643907", "4219540" ]
[ "nonn", "more" ]
16
0
4
[ "A006385", "A006389", "A006392", "A006393", "A379434" ]
[ "M3367" ]
N. J. A. Sloane
2025-01-16T14:17:31
oeisdata/seq/A006/A006393.seq
4126a4c375cf1ebafa4b68cac2bbd61a
A006394
Number of sensed planar maps with n edges and without loops or parallel edges.
[ "1", "1", "1", "3", "5", "15", "52", "213", "1002", "5167", "27967", "158447", "926786" ]
[ "nonn", "more" ]
26
0
4
[ "A006384", "A006390", "A006394", "A006395", "A022558" ]
[ "M2498" ]
N. J. A. Sloane
2025-01-16T16:26:45
oeisdata/seq/A006/A006394.seq
faec4f2c3dda8d82e1f2810c8fcbb6b8
A006395
Number of unsensed planar maps with n edges and without loops or parallel edges.
[ "1", "1", "1", "3", "5", "14", "42", "150", "624", "2947", "15079", "82607", "474030" ]
[ "nonn", "more" ]
23
0
4
[ "A006385", "A006391", "A006394", "A006395", "A022558" ]
[ "M2494" ]
N. J. A. Sloane
2025-01-16T16:17:44
oeisdata/seq/A006/A006395.seq
a83c76bf99ab5c6bc61edb46f8b29680
A006396
Number of sensed planar maps with n edges and without faces or vertices of degree 1.
[ "1", "0", "1", "2", "4", "10", "36", "132", "616", "3060", "16207", "88990", "503816" ]
[ "nonn", "more" ]
23
0
4
[ "A006384", "A006388", "A006396", "A006397", "A379435" ]
[ "M1238" ]
N. J. A. Sloane
2025-01-16T14:17:43
oeisdata/seq/A006/A006396.seq
c428de1024f953bd4cb8d84d8da3228c
A006397
Number of unsensed planar maps with n edges and without faces or vertices of degree 1.
[ "1", "0", "1", "2", "4", "10", "34", "114", "475", "2104", "10177", "52012", "279874" ]
[ "nonn", "more" ]
21
0
4
[ "A006385", "A006389", "A006396", "A006397", "A379435" ]
[ "M1236" ]
N. J. A. Sloane
2025-01-16T14:17:46
oeisdata/seq/A006/A006397.seq
010b2b9b9a9ca7561f75322959ffb793
A006398
Number of sensed planar maps with n edges and without loops or isthmuses.
[ "1", "0", "1", "2", "4", "8", "29", "92", "403", "1846", "9239", "48028", "259567" ]
[ "nonn", "more" ]
18
0
4
[ "A006384", "A006390", "A006398", "A006399", "A099553" ]
[ "M1163" ]
N. J. A. Sloane
2025-01-16T14:17:50
oeisdata/seq/A006/A006398.seq
2dd6dc823d7eb147adc1df66c5774a97
A006399
Number of unsensed planar maps with n edges and without loops or isthmuses.
[ "1", "0", "1", "2", "4", "8", "27", "76", "295", "1188", "5462", "26580", "138110" ]
[ "nonn", "more" ]
17
0
4
[ "A006385", "A006391", "A006398", "A006399", "A099553" ]
[ "M1162" ]
N. J. A. Sloane
2025-01-16T14:17:53
oeisdata/seq/A006/A006399.seq
27e972bb9f32a9553f344601183ed9fd
A006400
Number of sensed simple planar maps with n edges and without vertices of degree 1.
[ "1", "0", "0", "1", "1", "2", "5", "11", "33", "117", "431", "1755", "7485" ]
[ "nonn", "more" ]
26
0
6
[ "A006384", "A006388", "A006394", "A006400", "A006401", "A379436" ]
[ "M1404" ]
N. J. A. Sloane
2025-01-16T16:21:54
oeisdata/seq/A006/A006400.seq
90ab5f51155d560e83f2c6626cd144fe