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A174644
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Number of ways to place 5 nonattacking amazons (superqueens) on a 5 X n board.
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4
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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
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OFFSET
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1,8
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COMMENTS
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An amazon (superqueen) moves like a queen and a knight.
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LINKS
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FORMULA
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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