A195593 Number of ways to place 5n nonattacking kings on a vertical cylinder 10 X 2n.

64, 732, 4392, 18890, 66532, 205628, 580664, 1536814, 3877300, 9434784, 22327496, 51698178, 117645348, 263992580, 585640568, 1286898262, 2805399156, 6074441896, 13076687560, 28009586346, 59732295204, 126891641612, 268638308152, 566987715710

Offset: 1

Author

Vaclav Kotesovec, Sep 21 2011

Keywords

• nonn

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 10 are in contact (number of columns = 10, number of rows = 2n).

Links

• Ray Chandler, Table of n, a(n) for n = 1..3299 (first 1000 terms from Jinyuan Wang)
• Vaclav Kotesovec, Non-attacking chess pieces
• Index entries for linear recurrences with constant coefficients, signature (8,-26,44,-41,20,-4).

Crossrefs

Cf. A194647, A173783, A137432.

Programs

Mathematica

LinearRecurrence[{8, -26, 44, -41, 20, -4}, {64, 732, 4392, 18890, 66532, 205628}, 20] (* Jinyuan Wang, Feb 26 2020 *)

Formula

a(n) = -4*a(n-6) + 20*a(n-5) - 41*a(n-4) + 44*a(n-3) - 26*a(n-2) + 8*a(n-1).

G.f.: (1 + 56*x + 246*x^2 + 156*x^3 + 11*x^4)/((x-1)^4*(2*x-1)^2).

a(n) = (1771*n - 8709)*2^n + 235/3*n^3 + 880*n^2 + 12815/3*n + 8710.