A195657 Number of ways to place 8n nonattacking kings on a vertical cylinder 16 X 2n.

512, 17536, 218052, 1599820, 8500668, 36383284, 133538996, 437500380, 1314748124, 3694894500, 9849731140, 25173962492, 62193359676, 149475988116, 351246183572, 810197361564, 1840289301660, 4126688132548, 9154339355684, 20122502355004, 43888598831484

Offset: 1

Author

Vaclav Kotesovec, Sep 22 2011

Keywords

• nonn

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 16 are in contact (number of columns = 16, number of rows = 2n).

Links

• V. Kotesovec, Non-attacking chess pieces
• Index entries for linear recurrences with constant coefficients, signature (11, -53, 147, -259, 301, -231, 113, -32, 4).

Crossrefs

Cf. A195652, A174558, A137432.

Formula

Recurrence: a(n) = 4*a(n-9) - 32*a(n-8) + 113*a(n-7) - 231*a(n-6) + 301*a(n-5) - 259*a(n-4) + 147*a(n-3) - 53*a(n-2) + 11*a(n-1).

G.f.: -(1 + 501*x + 11957*x^2 + 52145*x^3 + 55651*x^4 + 13919*x^5 + 695*x^6 + 27*x^7)/((x-1)^7*(2*x-1)^2).

a(n) = (1751437*n - 15876635)*2^n + 8431/45*n^6 + 22263/5*n^5 + 500633/9*n^4 + 1381699/3*n^3 + 117001024/45*n^2 + 138801256/15*n + 15876636.