A195659 Number of ways to place 10n nonattacking kings on a vertical cylinder 20 X 2n.

2048, 148352, 3076180, 33175486, 239238888, 1314160492, 5937279840, 23174548666, 80812754568, 257860425672, 766319864440, 2149806985106, 5753007728148, 14807729805472, 36902750545260, 89523360235366, 212335537312668, 494171055510052, 1131839140825580

Offset

1,1

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 20 are in contact (number of columns = 20, number of rows = 2n).

Links

Table of n, a(n) for n=1..19.

V. Kotesovec, Non-attacking chess pieces

Formula

Recurrence: a(n) = 4*a(n-11) - 40*a(n-10) + 181*a(n-9) - 489*a(n-8) + 876*a(n-7) - 1092*a(n-6) + 966*a(n-5) - 606*a(n-4) + 264*a(n-3) - 76*a(n-2) + 13*a(n-1).

G.f.: -(1 + 2035*x + 121804*x^2 + 1302988*x^3 + 3919832*x^4 + 3822444*x^5 + 1204400*x^6 + 113216*x^7 + 3167*x^8 + 13*x^9)/((x-1)^9*(2*x-1)^2).

a(n) = (296191755*n - 3519976573)*2^n + 524495/2016*n^8 + 4217363/504*n^7 + 2363921/16*n^6 + 66422455/36*n^5 + 557314865/32*n^4 + 8943856601/72*n^3 + 322704776641/504*n^2 + 90034143925/42*n + 3519976574.

Crossrefs

Cf. A195654, A195649, A137432.

Sequence in context: A351162 A100629 A247934 * A321835 A017686 A008455

Adjacent sequences: A195656 A195657 A195658 * A195660 A195661 A195662

Keyword

nonn

Author

Vaclav Kotesovec, Sep 22 2011

Status

approved