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A174644
Number of ways to place 5 nonattacking amazons (superqueens) on a 5 X n board.
4
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
1,8
COMMENTS
An amazon (superqueen) moves like a queen and a knight.
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.
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 *)
CROSSREFS
Cf. A174642.
Sequence in context: A270099 A271274 A271286 * A273310 A229088 A270088
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Mar 25 2010
EXTENSIONS
More terms from Vincenzo Librandi, May 30 2013
STATUS
approved