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A177759
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Number of ways to place 6 nonattacking bishops on an n X n toroidal board.
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4
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0, 0, 0, 0, 0, 2304, 35280, 811008, 5080320, 38784000, 153679680, 699678720, 2120152320, 7113012480, 18036018000, 49416536064, 110279070720, 261526745088, 530024705280, 1128038400000
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OFFSET
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1,6
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2, 10, -22, -44, 110, 110, -330, -165, 660, 132, -924, 0, 924, -132, -660, 165, 330, -110, -110, 44, 22, -10, -2, 1).
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FORMULA
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Explicit formula: 1/1440*(n-4)^2*(n-2)^2*n^2*(2*n^6 -36*n^5 +269*n^4 -1128*n^3 +3143*n^2-6330*n +7425 +(15*n^4 -240*n^3 +1545*n^2 -4950*n +6975)*(-1)^n).
G.f.: -48*x^6*(15*x^17 +2386*x^16 +6778*x^15 +133898*x^14 +235216*x^13 +1520054*x^12 +1844806*x^11 +5402462*x^10+4378450*x^9 +6819710*x^8 +3509350*x^7 +3079094*x^6+926032*x^5 +445642*x^4 +65754*x^3 +14946*x^2 +639*x+48)/((x-1)^13*(x+1)^11).
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MATHEMATICA
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CoefficientList[Series[- 48 x^5 * (15 x^17 + 2386 x^16 + 6778 x^15 + 133898 x^14 + 235216 x^13 + 1520054 x^12 + 1844806 x^11 + 5402462 x^10 + 4378450 x^9 + 6819710 x^8 + 3509350 x^7 + 3079094 x^6 + 926032 x^5 + 445642 x^4 + 65754 x^3 + 14946 x^2 + 639 x + 48) / ((x - 1)^13 (x+1)^11), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)
LinearRecurrence[{2, 10, -22, -44, 110, 110, -330, -165, 660, 132, -924, 0, 924, -132, -660, 165, 330, -110, -110, 44, 22, -10, -2, 1}, {0, 0, 0, 0, 0, 2304, 35280, 811008, 5080320, 38784000, 153679680, 699678720, 2120152320, 7113012480, 18036018000, 49416536064, 110279070720, 261526745088, 530024705280, 1128038400000, 2120098821120, 4148067559680, 7337013702480, 13421018603520}, 30] (* Harvey P. Dale, Aug 20 2024 *)
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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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