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A172201
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Number of ways to place 3 nonattacking amazons (superqueens) on an n X n board.
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5
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0, 0, 0, 0, 48, 424, 1976, 6616, 17852, 41544, 86660, 166288, 298616, 508200, 827168, 1296744, 1968676, 2907016, 4189772, 5910944, 8182400, 11136168, 14926536, 19732600, 25760588, 33246664, 42459476, 53703216, 67320392, 83695144
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OFFSET
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1,5
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COMMENTS
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An amazon (superqueen) moves like a queen and a knight.
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REFERENCES
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Panos Louridas, idee & form 93/2007, pp. 2936-2938.
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LINKS
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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
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FORMULA
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Explicit formula (Panos Louridas, 2007): a(n) = (2n^6 - 20n^5 + 31n^4 + 314n^3 - 1452n^2 + 2040n - 672)/12 if n is even (n >= 4) and a(n) = (2n^6 - 20n^5 + 31n^4 + 314n^3 - 1452n^2 + 2034n - 669)/12 if n is odd (n >= 5).
G.f.: 4x^5*(x^7-7x^6+13x^5+23x^4-32x^3-60x^2-46x-12)/((x+1)^2*(x-1)^7). [Vaclav Kotesovec, Mar 24 2010]
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MATHEMATICA
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CoefficientList[Series[4 x^4 (x^7 - 7 x^6 + 13 x^5 + 23 x^4 - 32 x^3 - 60 x^2 - 46 x - 12) / ((x + 1)^2 (x - 1)^7), {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)
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CROSSREFS
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Cf. A051223, A051224, A047659, A061989, A172200.
Sequence in context: A019558 A339761 A232917 * A249293 A281374 A190416
Adjacent sequences: A172198 A172199 A172200 * A172202 A172203 A172204
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KEYWORD
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nonn,easy
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AUTHOR
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Vaclav Kotesovec, Jan 29 2010
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STATUS
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approved
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