A195592 Number of ways to place 4n nonattacking kings on a vertical cylinder 8 X 2n.

32, 256, 1220, 4460, 13932, 39316, 103508, 259372, 626780, 1473764, 3392964, 7682812, 17166476, 37942900, 83115188, 180699980, 390351420, 838619524, 1793087780, 3817890076, 8099228012, 17125372436, 36104600340, 75916936300, 159249370652, 333329766436

Offset: 1

Author

Vaclav Kotesovec, Sep 21 2011

Keywords

• nonn

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 8 are in contact (number of columns = 8, number of rows = 2n).

Links

• Ray Chandler, Table of n, a(n) for n = 1..3302
• V. Kotesovec, Non-attacking chess pieces
• Index entries for linear recurrences with constant coefficients, signature (7, -19, 25, -16, 4).

Crossrefs

Cf. A194646, A173782, A137432.

Programs

Mathematica

LinearRecurrence[{7,-19,25,-16,4},{32,256,1220,4460,13932},30] (* Harvey P. Dale, Jan 15 2016 *)

Formula

Recurrence: a(n) = 4*a(n-5) - 16*a(n-4) + 25*a(n-3) - 19*a(n-2) + 7*a(n-1).

G.f.: -(1 + 25*x + 51*x^2 + 11*x^3)/((x-1)^3*(2*x-1)^2).

a(n) = (221*n - 779)*2^n + 44*n^2 + 324*n + 780.