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%I #14 Aug 05 2024 10:25:04
%S 0,0,0,88,785,3528,11151,28560,63513,127520,236863,413736,687505,
%T 1096088,1687455,2521248,3670521,5223600,7286063,9982840,13460433,
%U 17889256,23466095,30416688,38998425,49503168,62260191,77639240,96053713,117963960,143880703
%N Number of ways to place 3 nonattacking kings on an n X n cylindrical chessboard.
%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 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F a(n) = 1/6*n*(n^5 - 27*n^3 + 18*n^2 + 194*n - 228), n>=4.
%F G.f.: -x^4*(15*x^6 - 89*x^5 + 196*x^4 - 140*x^3 - 119*x^2 + 169*x + 88)/(x-1)^7.
%t CoefficientList[Series[-x^3*(15*x^6 - 89*x^5 + 196*x^4 - 140*x^3 - 119*x^2 + 169*x + 88)/(x - 1)^7, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Dec 27 2023 *)
%Y Cf. A061996, A179404, A194650.
%K nonn
%O 1,4
%A _Vaclav Kotesovec_, Aug 31 2011