A195595 Number of ways to place 7n nonattacking kings on a vertical cylinder 14 X 2n.

256, 6060, 58776, 358564, 1649420, 6286658, 20984924, 63558566, 178909300, 476033636, 1212120160, 2980927200, 7129922604, 16675350430, 38293956836, 86629645122, 193553210580, 427974677968, 938053730248, 2040792091884, 4411561365324, 9483844861978

Offset

1,1

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 14 are in contact (number of columns = 14, number of rows = 2n).

Links

Table of n, a(n) for n=1..22.

V. Kotesovec, Non-attacking chess pieces

Formula

Recurrence: a(n) = -4*a(n-8) + 28*a(n-7) - 85*a(n-6) + 146*a(n-5) - 155*a(n-4) + 104*a(n-3) - 43*a(n-2) + 10*a(n-1).

G.f.: (1 + 246*x + 3543*x^2 + 9080*x^3 + 4915*x^4 + 442*x^5 + 15*x^6)/((x-1)^6*(2*x-1)^2).

a(n) = (157823*n - 1211433)*2^n + 9121/60*n^5 + 35581/12*n^4 + 352625/12*n^3 + 2179835/12*n^2 + 20456597/30*n + 1211434.

Crossrefs

Cf. A195004, A174155, A137432.

Sequence in context: A196152 A113173 A223964 * A204567 A077072 A283339

Adjacent sequences: A195592 A195593 A195594 * A195596 A195597 A195598

Keyword

nonn

Author

Vaclav Kotesovec, Sep 21 2011

Status

approved