A201242 Number of ways to place 8 non-attacking wazirs on an n X n toroidal board.

0, 0, 0, 2, 1550, 546516, 28482279, 585632520, 6829066665, 54504255500, 331490619174, 1642426038486, 6930083422496, 25686190415144, 85541928717375, 260349711114720, 733731834393719, 1934755847570808, 4813391235753128, 11375736647373750, 25684539545337246

Offset

1,4

Comments

Wazir is a leaper [0,1].

Links

Table of n, a(n) for n=1..21.

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

Formula

a(n) = n^2*(n^14 - 140n^12 + 8722n^10 - 313880n^8 + 7061089n^6 - 99573740n^4 + 817978188n^2 - 3033601200)/40320, n>=9.

G.f.: x^4 * (16x^21 - 566x^20 + 8182x^19 - 67700x^18 + 377824x^17 - 1531112x^16 + 4601788x^15 - 10205035x^14 + 16637339x^13 - 21628151x^12 + 32135719x^11 - 68863352x^10 + 138461546x^9 - 189569712x^8 + 133644570x^7 + 20663373x^6 - 378949513x^5 - 174710713x^4 - 19400947x^3 - 520438x^2 - 1516x - 2)/(x-1)^17.

Crossrefs

Cf. A201236, A201237, A201238, A201239, A201240, A201241.

Sequence in context: A179866 A296362 A282999 * A062585 A239505 A002490

Adjacent sequences: A201239 A201240 A201241 * A201243 A201244 A201245

Keyword

nonn

Author

Vaclav Kotesovec, Nov 28 2011

Status

approved