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A035291
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Number of ways to place a non-attacking white and black queen on n X n chessboard.
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2
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0, 0, 16, 88, 280, 680, 1400, 2576, 4368, 6960, 10560, 15400, 21736, 29848, 40040, 52640, 68000, 86496, 108528, 134520, 164920, 200200, 240856, 287408, 340400, 400400, 468000, 543816, 628488, 722680, 827080, 942400, 1069376, 1208768
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = (3 n^4 - 10 n^3 + 9 n^2 - 2 n)/3.
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EXAMPLE
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There are 16 ways of putting distinct queens on 3 X 3 so that neither can capture the other.
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MATHEMATICA
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CoefficientList[Series[8*x^3*(2+x)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 22 2012 *)
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PROG
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(Magma) [(3*n^4-10*n^3+9*n^2-2*n)/3: n in [1..40]]; // Vincenzo Librandi, Apr 22 2012
(Magma) I:=[0, 0, 16, 88, 280]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Apr 22 2012
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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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STATUS
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approved
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