A174644 Number of ways to place 5 nonattacking amazons (superqueens) on a 5 X n board.

0, 0, 0, 0, 0, 0, 0, 4, 40, 204, 708, 1968, 4712, 10064, 19656, 35744, 61328, 100272, 157424, 238736, 351384, 503888, 706232, 969984, 1308416, 1736624, 2271648, 2932592, 3740744, 4719696, 5895464, 7296608, 8954352, 10902704, 13178576, 15821904

Offset: 1

Author

Vaclav Kotesovec, Mar 25 2010

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes
• The Oprisch Family Web Site

Crossrefs

Cf. A174642.

Programs

Mathematica

CoefficientList[Series[4 x^7 (x^9 + x^8 + 7 x^7 - 6 x^6 + 5 x^5 + 10 x^4 + x^3 + 6 x^2 + 4 x + 1) / (x - 1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)

Formula

G.f.: 4*x^8*(x^9+x^8+7*x^7-6*x^6+5*x^5+10*x^4+x^3+6*x^2+4*x+1)/(x-1)^6.

Explicit formula: a(n) = n^5-44n^4+823n^3-8168n^2+42796n -93984, n>=12.

Extensions

More terms from Vincenzo Librandi, May 30 2013