A174642 Number of ways to place 4 nonattacking amazons (superqueens) on a 4 X n board.

0, 0, 0, 0, 0, 0, 0, 12, 60, 180, 432, 900, 1692, 2940, 4800, 7452, 11100, 15972, 22320, 30420, 40572, 53100, 68352, 86700, 108540, 134292, 164400, 199332, 239580, 285660, 338112, 397500, 464412, 539460, 623280, 716532, 819900, 934092, 1059840

Offset

1,8

Comments

An amazon (superqueen) moves like a queen and a knight

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

The Oprisch Family Web Site

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Formula

G.f.: -12*x^8*(x^3+1)/(x-1)^5.

Explicit formula: a(n) = (n-7)(n^3-21n^2+158n-420), n>=7.

Mathematica

CoefficientList[Series[- 12 x^7 (x^3 + 1) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)

Crossrefs

Cf. A173214, A172201, A172200, A051223, A051224, A036464.

Sequence in context: A008530 A033486 A112415 * A061624 A213818 A004302

Adjacent sequences: A174639 A174640 A174641 * A174643 A174644 A174645

Keyword

nonn,easy

Author

Vaclav Kotesovec, Mar 25 2010

Extensions

More terms from Vincenzo Librandi, May 30 2013

Status

approved