cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A194648 Number of ways to place 6n nonattacking kings on a 12 X 2n cylindrical chessboard.

Original entry on oeis.org

448, 1732, 7918, 39316, 205628, 1118398, 6286658, 36383284, 216134044, 1314160492, 8155899320, 51526819510, 330559583178, 2148524237842, 14120142260138, 93669254201140, 626289974615094, 4215364545901036, 28531464984810918, 194028126730583796
Offset: 1

Views

Author

Vaclav Kotesovec, Aug 31 2011

Keywords

Comments

This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 12, number of rows = 2n).

Links

  • Ray Chandler, Table of n, a(n) for n = 1..1182
  • V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights
  • Vaclav Kotesovec, G.f., recurrence and explicit formula
  • Index entries for linear recurrences with constant coefficients, signature (123, -7321, 280953, -7815096, 167948132, -2902322885, 41450235787, -499005760654, 5139688443504, -45815780494341, 356686744049422, -2442977988253415, 14807521518627422, -79813193163925620, 384075945698236159, -1655461203049171846, 6408095608117333736, -22324060511037585983, 70110767534529096739, -198758740577568913437, 509105053427808565774, -1178957762144560119277, 2469102261987638350625, -4676788353519183205994, 8009846446628877143184, -12398045659209581154381, 17330242433059284917247, -21854027730161965985121, 24829391878777653306741, -25375425632156076733736, 23283124318667970185580, -19136737348463193623732, 14052187658858602811086, -9190302655918861018594, 5334155219056391326621, -2736099335631729732358, 1234232572662337908295, -486797186990900726158, 166723091105251092029, -49174878927647152193, 12365157710942649267, -2617610437109862140, 459103033290045078, -65327706620774553, 7328352058508736, -621736878459564, 37366066553760, -1412422401600, 25147584000).

Crossrefs

Cf. A174154, A194644, A194645, A194646, A194647, A137432, A195594.

Formula

Asymptotic: a(n) ~ 2*7^n.

A195004 Number of ways to place 7n nonattacking kings on a 14 X 2n cylindrical chessboard.

Original entry on oeis.org

1024, 4100, 19648, 103508, 580664, 3419648, 20984924, 133538996, 877751236, 5937279840, 41180193352, 291859775552, 2106967145904, 15448890481568, 114765555945488, 861942483797204, 6533144250310688, 49899718750389380, 383593821097441412, 2964842429047018248
Offset: 1

Views

Author

Vaclav Kotesovec, Sep 07 2011

Keywords

Comments

This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 14, number of rows = 2n).

Links

  • Ray Chandler, Table of n, a(n) for n = 1..1106
  • V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights
  • Vaclav Kotesovec, G.f., recurrence and explicit formula
  • Index entries for linear recurrences with constant coefficients, signature (234, -26876, 2019709, -111697218, 4847894553, -171967643248, 5126864261813, -131103713766739, 2920551204572253, -57369727964797769, 1003499987301575705, -15756273391572396056, 223560731166583964170, -2882674835842994926649, 33942752076287377374732, -366481987107253117428678, 3641474337928260994018833, -33403183417194915064568472, 283651397179433118312259120, -2235256807858321803493302712, 16381469343464643012631705641, -111864817301276143786034674593, 713000590137978010047099019123, -4248167585872182220244662296078, 23692825139854478095829187332583, -123839650151492238580849239743842, 607291338747966869409975798808119, -2796687736808231684915622029956501, 12105097441367664211274616723997585, -49282739018956175502285900368718340, 188846441297378176522518597171831038, -681488797315874299501618146366584502, 2317175918409451996565304916085049225, -7426636629919740985496045649451822465, 22444540561400607122897712881328419731, -63979187901854273527092491251827548655, 172057350932125535425088191059644660790, -436601690854837262203616552560815387262, 1045493932598927036221255467761014916672, -2362673225064751662372547547704555633600, 5038838587531054046651836530047833987628, -10140921814167342121211938118088849001792, 19257391087913181405263225040629151186272, -34500132785018636006710664752520219397318, 58298198399790056471455253509791714097825, -92893574441178572445869535970403724406464, 139532260661304247096543190046679153931782, -197497210344518691909307839617377332496726, 263305424445938364650937820234766261392812, -330492584893065300696048626280270629928420, 390329890315638397879899046383015257779768, -433519474585554675321027469844536795515096, 452483527667626510122157361959823577545116, -443501901490900685964486690632625788788496, 407883969421282557544660851181757217890384, -351675933152655222446863110197897961028664, 283984050472933807032016387053214808490768, -214551731812442749852409765446269884375456, 151480235225815576544104717761138879307344, -99820208079286562792944814404190179497760, 61308554282442277738368818159312699696768, -35043595589343382666629911544555460702048, 18610707623818189757146652551568358579392, -9166308055333364648206086359099895891840, 4178629157017923157800455107231658228096, -1759220243521242971272733964440808344960, 682319955535117483948474380530632894464, -243136873223743567485233920640254062592, 79356174222862273290100936536508525568, -23641977426444551429474710014044615168, 6404251284485474979502046840644695040, -1570379926552348612740435108569370624, 346795140719354500498066916678473728, -68563667046969861210140030991157248, 12051369611781880146558356044689408, -1867616610183259872317123737116672, 252622266308749887603294277730304, -29456297112310112325526951329792, 2914402636658640861712637558784, -239667516215588644643093741568, 15925650465805208711732920320, -820834685159380646929367040, 30762599549292146117836800, -745091435273014738944000, 8746516217730170880000).

Crossrefs

Cf. A174155, A194644, A194645, A194646, A194647, A194648, A137432, A195595.

A195593 Number of ways to place 5n nonattacking kings on a vertical cylinder 10 X 2n.

Original entry on oeis.org

64, 732, 4392, 18890, 66532, 205628, 580664, 1536814, 3877300, 9434784, 22327496, 51698178, 117645348, 263992580, 585640568, 1286898262, 2805399156, 6074441896, 13076687560, 28009586346, 59732295204, 126891641612, 268638308152, 566987715710
Offset: 1

Views

Author

Vaclav Kotesovec, Sep 21 2011

Keywords

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 10 are in contact (number of columns = 10, number of rows = 2n).

Links

Crossrefs

Cf. A194647, A173783, A137432.

Programs

  • Mathematica
    LinearRecurrence[{8, -26, 44, -41, 20, -4}, {64, 732, 4392, 18890, 66532, 205628}, 20] (* Jinyuan Wang, Feb 26 2020 *)

Formula

a(n) = -4*a(n-6) + 20*a(n-5) - 41*a(n-4) + 44*a(n-3) - 26*a(n-2) + 8*a(n-1).
G.f.: (1 + 56*x + 246*x^2 + 156*x^3 + 11*x^4)/((x-1)^4*(2*x-1)^2).
a(n) = (1771*n - 8709)*2^n + 235/3*n^3 + 880*n^2 + 12815/3*n + 8710.
Showing 1-3 of 3 results.

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