A195594 Number of ways to place 6n nonattacking kings on a vertical cylinder 12 X 2n.

128, 2102, 15988, 81606, 327192, 1118398, 3419648, 9643562, 25603228, 64923594, 158877948, 378088270, 879980720, 2011806182, 4532900488, 10091643138, 22244251284, 48622120786, 105526014500, 227633451206, 488451508168, 1043298475662, 2219419264848

Offset

1,1

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 12 are in contact (number of columns = 12, number of rows = 2n).

Links

Table of n, a(n) for n=1..23.

V. Kotesovec, Non-attacking chess pieces

Formula

Recurrence: a(n) = 4*a(n-7) - 24*a(n-6) + 61*a(n-5) - 85*a(n-4) + 70*a(n-3) - 34*a(n-2) + 9*a(n-1).

G.f.: -(1 + 119*x + 984*x^2 + 1352*x^3 + 307*x^4 + 9*x^5)/((x-1)^5*(2*x-1)^2).

a(n) = (15839*n - 99729)*2^n + 231/2*n^4 + 1767*n^3 + 26001/2*n^2 + 53295*n + 99730.

Crossrefs

Cf. A194648, A174154, A137432.

Sequence in context: A093528 A283338 A128696 * A321831 A351195 A223954

Adjacent sequences: A195591 A195592 A195593 * A195595 A195596 A195597

Keyword

nonn

Author

Vaclav Kotesovec, Sep 21 2011

Status

approved