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%I #16 Aug 17 2024 15:32:06
%S 32,256,1220,4460,13932,39316,103508,259372,626780,1473764,3392964,
%T 7682812,17166476,37942900,83115188,180699980,390351420,838619524,
%U 1793087780,3817890076,8099228012,17125372436,36104600340,75916936300,159249370652,333329766436
%N Number of ways to place 4n nonattacking kings on a vertical cylinder 8 X 2n.
%C Vertical cylinder: a chessboard where it is supposed that the columns 1 and 8 are in contact (number of columns = 8, number of rows = 2n).
%H Ray Chandler, <a href="/A195592/b195592.txt">Table of n, a(n) for n = 1..3302</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7, -19, 25, -16, 4).
%F Recurrence: a(n) = 4*a(n-5) - 16*a(n-4) + 25*a(n-3) - 19*a(n-2) + 7*a(n-1).
%F G.f.: -(1 + 25*x + 51*x^2 + 11*x^3)/((x-1)^3*(2*x-1)^2).
%F a(n) = (221*n - 779)*2^n + 44*n^2 + 324*n + 780.
%t LinearRecurrence[{7,-19,25,-16,4},{32,256,1220,4460,13932},30] (* _Harvey P. Dale_, Jan 15 2016 *)
%Y Cf. A194646, A173782, A137432.
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, Sep 21 2011