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%I #14 Aug 17 2024 15:46:33
%S 256,6060,58776,358564,1649420,6286658,20984924,63558566,178909300,
%T 476033636,1212120160,2980927200,7129922604,16675350430,38293956836,
%U 86629645122,193553210580,427974677968,938053730248,2040792091884,4411561365324,9483844861978
%N Number of ways to place 7n nonattacking kings on a vertical cylinder 14 X 2n.
%C Vertical cylinder: a chessboard where it is supposed that the columns 1 and 14 are in contact (number of columns = 14, number of rows = 2n).
%H Ray Chandler, <a href="/A195595/b195595.txt">Table of n, a(n) for n = 1..3292</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (10, -43, 104, -155, 146, -85, 28, -4).
%F Recurrence: a(n) = -4*a(n-8) + 28*a(n-7) - 85*a(n-6) + 146*a(n-5) - 155*a(n-4) + 104*a(n-3) - 43*a(n-2) + 10*a(n-1).
%F G.f.: (1 + 246*x + 3543*x^2 + 9080*x^3 + 4915*x^4 + 442*x^5 + 15*x^6)/((x-1)^6*(2*x-1)^2).
%F a(n) = (157823*n - 1211433)*2^n + 9121/60*n^5 + 35581/12*n^4 + 352625/12*n^3 + 2179835/12*n^2 + 20456597/30*n + 1211434.
%Y Cf. A195004, A174155, A137432.
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, Sep 21 2011