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A061990
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Number of ways to place 4 nonattacking queens on a 4 X n board.
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15
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0, 0, 0, 0, 2, 12, 46, 140, 344, 732, 1400, 2468, 4080, 6404, 9632, 13980, 19688, 27020, 36264, 47732, 61760, 78708, 98960, 122924, 151032, 183740, 221528, 264900, 314384, 370532, 433920, 505148, 584840, 673644, 772232, 881300, 1001568, 1133780, 1278704, 1437132
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: -2*x^4*(x^3-x^2+x+1)*(x^4+4*x^2+1)/(x-1)^5.
Recurrence: a(n)=5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5), n >= 12.
Explicit formula (H. Tarry, 1890): a(n)=n^4-18*n^3+139*n^2-534*n+840, n >= 7.
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MATHEMATICA
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Join[{0, 0, 0, 0, 2, 12, 46}, LinearRecurrence[{5, -10, 10, -5, 1}, {140, 344, 732, 1400, 2468}, 30]] (* Harvey P. Dale, Mar 06 2013 *)
CoefficientList[Series[-2 x^4 (x^3 - x^2 + x + 1) (x^4 + 4 x^2 + 1) / (x-1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, May 02 2013 *)
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PROG
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(PARI) a(n)=if(n<7, [0, 0, 0, 0, 2, 12, 46][n+1], n^4-18*n^3+139*n^2-534*n+840) \\ Charles R Greathouse IV, Oct 21 2022
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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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Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 29 2001
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STATUS
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approved
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