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%I #24 Aug 17 2024 15:39:17
%S 64,732,4392,18890,66532,205628,580664,1536814,3877300,9434784,
%T 22327496,51698178,117645348,263992580,585640568,1286898262,
%U 2805399156,6074441896,13076687560,28009586346,59732295204,126891641612,268638308152,566987715710
%N Number of ways to place 5n nonattacking kings on a vertical cylinder 10 X 2n.
%C 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).
%H Ray Chandler, <a href="/A195593/b195593.txt">Table of n, a(n) for n = 1..3299</a> (first 1000 terms from Jinyuan Wang)
%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (8,-26,44,-41,20,-4).
%F 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).
%F G.f.: (1 + 56*x + 246*x^2 + 156*x^3 + 11*x^4)/((x-1)^4*(2*x-1)^2).
%F a(n) = (1771*n - 8709)*2^n + 235/3*n^3 + 880*n^2 + 12815/3*n + 8710.
%t LinearRecurrence[{8, -26, 44, -41, 20, -4}, {64, 732, 4392, 18890, 66532, 205628}, 20] (* _Jinyuan Wang_, Feb 26 2020 *)
%Y Cf. A194647, A173783, A137432.
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, Sep 21 2011