A194648 - OEIS

%I #18 Aug 17 2024 15:21:18

%S 448,1732,7918,39316,205628,1118398,6286658,36383284,216134044,

%T 1314160492,8155899320,51526819510,330559583178,2148524237842,

%U 14120142260138,93669254201140,626289974615094,4215364545901036,28531464984810918,194028126730583796

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

%C 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).

%H Ray Chandler, <a href="/A194648/b194648.txt">Table of n, a(n) for n = 1..1182</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens, kings, bishops and knights</a>

%H Vaclav Kotesovec, <a href="/A194648/a194648.txt">G.f., recurrence and explicit formula</a>

%H <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, 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).

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

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

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, Aug 31 2011