A194654 - OEIS

%I #12 Aug 06 2024 09:28:34

%S 0,0,0,0,125,28930,809368,9414152,66305781,338374560,1378426060,

%T 4751038284,14388638901,39296604844,98605016040,230507248912,

%U 507379370525,1060395103800,2118303772332,4066797540820,7537144196589,13535598398916,23628635128024,40203393674520

%N Number of ways to place 6 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_13">Index entries for linear recurrences with constant coefficients</a>, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

%F a(n) = 1/720*n*(n^11 - 135*n^9 + 90*n^8 + 7525*n^7 - 9420*n^6 - 216045*n^5 + 378090*n^4 + 3192694*n^3 - 6899520*n^2 - 19450080*n + 48327120), n>=7.

%F G.f.: x^5*(622*x^14 - 6966*x^13 + 37088*x^12 - 130876*x^11 + 344918*x^10 - 655255*x^9 + 737997*x^8 - 153262*x^7 - 639936*x^6 + 251910*x^5 + 1132096*x^4 - 1113158*x^3 - 443028*x^2 - 27305*x - 125)/(x-1)^13.

%Y Cf. A172158, A179426, A194650, A194651, A194652, A194653.

%K nonn

%O 1,5

%A _Vaclav Kotesovec_, Aug 31 2011