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A195660
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Number of ways to place 11n nonattacking kings on a vertical cylinder 22 X 2n.
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2
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4096, 433500, 11682296, 153802520, 1301236304, 8155899320, 41180193352, 176740657340, 668845118276, 2290966142762, 7241521734020, 21437333168798, 60123048359816, 161217291701134, 416373921218580, 1041997475699102, 2539265644237492, 6050425313244116
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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 22 are in contact (number of columns = 22, number of rows = 2n).
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LINKS
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FORMULA
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Recurrence: a(n) = -4*a(n-12) + 44*a(n-11) - 221*a(n-10) + 670*a(n-9) - 1365*a(n-8) + 1968*a(n-7) - 2058*a(n-6) + 1572*a(n-5) - 870*a(n-4) + 340*a(n-3) - 89*a(n-2) + 14*a(n-1).
G.f.: (1 + 4082*x + 376245*x^2 + 5977500*x^3 + 27440106*x^4 + 43897316*x^5 + 25742850*x^6 + 5340248*x^7 + 353057*x^8 + 5622*x^9 + 23*x^10)/((x-1)^10*(2*x-1)^2).
a(n) = (4480441703*n - 59644067185)*2^n + 10913705/36288*n^9 + 219791627/20160*n^8 + 6663742261/30240*n^7 + 1542837967/480*n^6 + 314791170001/8640*n^5 + 311982683023/960*n^4 + 6333872421866/2835*n^3 + 56561301500209/5040*n^2 + 46445710897861/1260*n + 59644067186.
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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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