A201241 Number of ways to place 7 non-attacking wazirs on an n X n toroidal board.

0, 0, 0, 16, 4450, 442980, 11281312, 139580160, 1103589198, 6433276500, 30047250222, 118507673088, 408912072478, 1265701033492, 3579712962750, 9380986518528, 23027843919870, 53409035159316, 117860600410206, 248890790976000, 505371757001454, 990655558290772

Offset

1,4

Comments

Wazir is a leaper [0,1].

Links

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

V. Kotesovec, Non-attacking chess pieces, 6ed, p.402

Formula

a(n) = n^2*(n^12 - 105*n^10 + 4795*n^8 - 122115*n^6 + 1834084*n^4 - 15461460*n^2 + 57441600)/5040, n>=8.

G.f.: -2*x^4 * (7*x^18 - 177*x^17 + 1965*x^16 - 12491*x^15 + 53736*x^14 - 175854*x^13 + 461641*x^12 - 942615*x^11 + 1320318*x^10 - 788656*x^9 - 1206129*x^8 + 3443471*x^7 - 3128600*x^6 - 552570*x^5 + 7435235*x^4 + 2548291*x^3 + 188955*x^2 + 2105*x + 8)/((x-1)^15).

Crossrefs

Cf. A201236, A201237, A201238, A201239, A201240, A201242.

Sequence in context: A272358 A176369 A090045 * A123280 A289904 A181028

Adjacent sequences: A201238 A201239 A201240 * A201242 A201243 A201244

Keyword

nonn

Author

Vaclav Kotesovec, Nov 28 2011

Status

approved