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%I #12 Dec 27 2023 13:01:25
%S 0,0,0,32,1205,13260,74494,291708,908973,2416410,5711530,12327414,
%T 24743693,46797968,84216990,145288600,241697109,389546478,610597338,
%U 933745570,1396771845,2048393204,2950649438,4181658708,5838778525,8042209890,10939084074,14708073198
%N Number of ways to place 4 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>
%F a(n) = 1/24*n*(n^7 - 54*n^5 + 36*n^4 + 1019*n^3 - 1236*n^2 - 6690*n + 10884), n>=5.
%F G.f.: x^4*(54*x^9 - 384*x^8 + 1052*x^7 - 1263*x^6 + 657*x^5 - 1434*x^4 + 4154*x^3 - 3567*x^2 - 917*x - 32)/(x-1)^9.
%t CoefficientList[Series[x^3*(54*x^9 - 384*x^8 + 1052*x^7 - 1263*x^6 + 657*x^5 - 1434*x^4 + 4154*x^3 - 3567*x^2 - 917*x - 32)/(x - 1)^9, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Dec 27 2023 *)
%Y Cf. A061997, A179424, A194650, A194651.
%K nonn
%O 1,4
%A _Vaclav Kotesovec_, Aug 31 2011
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