A194647 Number of ways to place 5n nonattacking kings on a 10 X 2n cylindrical chessboard.
192, 708, 3036, 13932, 66532, 327192, 1649420, 8500668, 44693472, 239238888, 1301236304, 7177627944, 40078823652, 226167613792, 1287874058656, 7390391650172, 42688584938548, 247956702607932, 1447080255512308, 8479116559291112, 49852445684576540
Offset: 1
Keywords
Links
- Ray Chandler, Table of n, a(n) for n = 1..1284
- V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights
- Vaclav Kotesovec, Explicit formula and recurrence
- Index entries for linear recurrences with constant coefficients, signature (56, -1460, 23541, -263028, 2162701, -13565686, 66416673, -257594833, 798883747, -1991743054, 4000492482, -6469161690, 8395031504, -8690399936, 7111450512, -4541105512, 2222092032, -811893408, 213097152, -37748736, 4020480, -193536).
Formula
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)).
Asymptotic: a(n) ~ 2*6^n.
Comments