A194653 - OEIS

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

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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

Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

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