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Number of ways to place 3n nonattacking kings on a vertical cylinder 6 X 2n.
2

%I #16 Aug 17 2024 15:30:11

%S 16,90,344,1082,3036,7918,19648,47058,109796,251126,565512,1257754,

%T 2769196,6046014,13107536,28246370,60555636,129237382,274727320,

%U 581960106,1228931516,2587886030,5435818464,11391730162,23823647236,49727668758,103616086568

%N Number of ways to place 3n nonattacking kings on a vertical cylinder 6 X 2n.

%C Vertical cylinder: a chessboard where it is supposed that the columns 1 and 6 are in contact (number of columns = 6, number of rows = 2n).

%H Ray Chandler, <a href="/A195591/b195591.txt">Table of n, a(n) for n = 1..3305</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).

%F Recurrence: a(n) = -4*a(n-4) + 12*a(n-3) - 13*a(n-2) + 6*a(n-1).

%F G.f.: (1+10*x+7*x^2)/((x-1)^2*(2*x-1)^2).

%F a(n) = (31*n - 65)*2^n + 18*n + 66.

%t LinearRecurrence[{6,-13,12,-4},{16,90,344,1082},30] (* _Harvey P. Dale_, Nov 15 2021 *)

%Y Cf. A194645, A061594, A137432.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, Sep 21 2011