A194653 Number of ways to place 5 nonattacking kings on an n X n cylindrical chessboard.

0, 0, 0, 0, 655, 26952, 309869, 1998752, 9124848, 33065040, 101473009, 274593648, 673080928, 1522931256, 3224953725, 6458355776, 12330557912, 22588294464, 39908439249, 68290845520, 113579839128, 184145882536, 291764365485, 452734505952, 689287992800

Offset

1,5

Links

Table of n, a(n) for n=1..25.

V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights

Formula

a(n) = 1/120*n*(n^9 - 90*n^7 + 60*n^6 + 3155*n^5 - 3900*n^4 - 50910*n^3 + 86580*n^2 + 318864*n - 656160), n>=6.

G.f.: -x^5*(185*x^11 - 1635*x^10 + 6336*x^9 - 15496*x^8 + 32185*x^7 - 62315*x^6 + 86237*x^5 - 49559*x^4 - 35522*x^3 + 49422*x^2 + 19747*x + 655)/(x-1)^11.

Crossrefs

Cf. A061998, A179425, A194650, A194651, A194652.

Sequence in context: A065759 A280445 A220057 * A252671 A252672 A252679

Adjacent sequences: A194650 A194651 A194652 * A194654 A194655 A194656

Keyword

nonn

Author

Vaclav Kotesovec, Aug 31 2011

Status

approved