A195590 Number of ways to place 2n nonattacking kings on a vertical cylinder 4 X 2n.

8, 32, 100, 276, 708, 1732, 4100, 9476, 21508, 48132, 106500, 233476, 507908, 1097732, 2359300, 5046276, 10747908, 22806532, 48234500, 101711876, 213909508, 448790532, 939524100, 1962934276, 4093640708, 8522825732, 17716740100, 36775657476, 76235669508

Offset: 1

Author

Vaclav Kotesovec, Sep 21 2011

Keywords

• nonn

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 4 are in contact (number of columns = 4, number of rows = 2n).

Links

• Ray Chandler, Table of n, a(n) for n = 1..3307
• V. Kotesovec, Non-attacking chess pieces
• Index entries for linear recurrences with constant coefficients, signature (5, -8, 4).

Crossrefs

Cf. A194644, A061593, A137432.

Formula

Recurrence: a(n) = 4*a(n-3) - 8*a(n-2) + 5*a(n-1).

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

Explicit formula: a(n) = (5*n-3)*2^n + 4.