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A174642
Number of ways to place 4 nonattacking amazons (superqueens) on a 4 X n board.
5
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
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
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Mar 25 2010
EXTENSIONS
More terms from Vincenzo Librandi, May 30 2013
STATUS
approved