A194654 Number of ways to place 6 nonattacking kings on an n X n cylindrical chessboard.

0, 0, 0, 0, 125, 28930, 809368, 9414152, 66305781, 338374560, 1378426060, 4751038284, 14388638901, 39296604844, 98605016040, 230507248912, 507379370525, 1060395103800, 2118303772332, 4066797540820, 7537144196589, 13535598398916, 23628635128024, 40203393674520

Offset

1,5

Links

Table of n, a(n) for n=1..24.

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

Formula

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.

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.

Crossrefs

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

Sequence in context: A036532 A086704 A163596 * A222277 A013783 A030697

Adjacent sequences: A194651 A194652 A194653 * A194655 A194656 A194657

Keyword

nonn

Author

Vaclav Kotesovec, Aug 31 2011

Status

approved