A194647 - OEIS

%I #18 Aug 17 2024 15:16:47

%S 192,708,3036,13932,66532,327192,1649420,8500668,44693472,239238888,

%T 1301236304,7177627944,40078823652,226167613792,1287874058656,

%U 7390391650172,42688584938548,247956702607932,1447080255512308,8479116559291112,49852445684576540

%N Number of ways to place 5n nonattacking kings on a 10 X 2n cylindrical chessboard.

%C This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 10, number of rows = 2n).

%H Ray Chandler, <a href="/A194647/b194647.txt">Table of n, a(n) for n = 1..1284</a>

%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 Vaclav Kotesovec, <a href="/A194647/a194647.txt">Explicit formula and recurrence</a>

%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (56, -1460, 23541, -263028, 2162701, -13565686, 66416673, -257594833, 798883747, -1991743054, 4000492482, -6469161690, 8395031504, -8690399936, 7111450512, -4541105512, 2222092032, -811893408, 213097152, -37748736, 4020480, -193536).

%F G.f.: -2*(7089408*x^21 - 132938496*x^20 + 1125112128*x^19 - 5717239392*x^18 + 19578445344*x^17 - 48082847384*x^16 + 88003026752*x^15 - 123138008952*x^14 + 134072006560*x^13 - 114991853490*x^12 + 78336556962*x^11 - 42596878318*x^10 + 18524447581*x^9 - 6435525481*x^8 + 1778018953*x^7 - 387290192*x^6 + 65568715*x^5 - 8436954*x^4 + 796245*x^3 - 51918*x^2 + 2088*x - 39)/((x-1)*(2*x-1)*(4*x-1)*(6*x-1)*(x^2-4*x+1)*(2*x^2-5*x+1)*(2*x^2-4*x+1)*(4*x^2-6*x+1)*(6*x^2-6*x+1)*(7*x^2-6*x+1)*(2*x^3-8*x^2+6*x-1)*(3*x^3-9*x^2+6*x-1)).

%F Asymptotic: a(n) ~ 2*6^n.

%Y Cf. A173783, A194644, A194645, A194646, A137432, A195593.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, Aug 31 2011