A174645 Number of ways to place 6 nonattacking amazons (superqueens) on a 6 X n board.

0, 0, 0, 0, 0, 0, 0, 0, 16, 170, 920, 3512, 10896, 29020, 68550, 147240, 292996, 547590, 970996, 1646446, 2686212, 4238086, 6492580, 9690846, 14133316, 20189062, 28305876, 39021070, 52972996, 70913286, 93719812, 122410366, 158157060, 202301446, 256370356, 322092462

Offset

1,9

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.: -2*x^9*(11*x^14-14*x^13+3*x^12+49*x^11-14*x^10-22*x^9+22*x^8+112*x^7+24*x^6-43*x^5+121*x^4+41*x^3+33*x^2+29*x+8)/(x-1)^7

Explicit formula: a(n) = n^6-63n^5+1775n^4-28613n^3+277462n^2-1526716n +3699966, n>=17.

Mathematica

CoefficientList[Series[- 2 x^8 (11 x^14 - 14 x^13 + 3 x^12 + 49 x^11 - 14 x^10 - 22 x^9 + 22 x^8 + 112 x^7 + 24 x^6 - 43 x^5 + 121 x^4 + 41 x^3 + 33 x^2 + 29 x + 8) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)

Crossrefs

Cf. A174642, A174644.

Sequence in context: A264092 A050628 A048557 * A021424 A200673 A230510

Adjacent sequences: A174642 A174643 A174644 * A174646 A174647 A174648

Keyword

nonn,easy

Author

Vaclav Kotesovec, Mar 25 2010

Extensions

More terms from Vincenzo Librandi, May 30 2013

Status

approved