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A195595
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Number of ways to place 7n nonattacking kings on a vertical cylinder 14 X 2n.
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1
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256, 6060, 58776, 358564, 1649420, 6286658, 20984924, 63558566, 178909300, 476033636, 1212120160, 2980927200, 7129922604, 16675350430, 38293956836, 86629645122, 193553210580, 427974677968, 938053730248, 2040792091884, 4411561365324, 9483844861978
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OFFSET
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1,1
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COMMENTS
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Vertical cylinder: a chessboard where it is supposed that the columns 1 and 14 are in contact (number of columns = 14, number of rows = 2n).
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LINKS
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FORMULA
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Recurrence: a(n) = -4*a(n-8) + 28*a(n-7) - 85*a(n-6) + 146*a(n-5) - 155*a(n-4) + 104*a(n-3) - 43*a(n-2) + 10*a(n-1).
G.f.: (1 + 246*x + 3543*x^2 + 9080*x^3 + 4915*x^4 + 442*x^5 + 15*x^6)/((x-1)^6*(2*x-1)^2).
a(n) = (157823*n - 1211433)*2^n + 9121/60*n^5 + 35581/12*n^4 + 352625/12*n^3 + 2179835/12*n^2 + 20456597/30*n + 1211434.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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