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A172124
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Number of ways to place 3 nonattacking bishops on an n X n board
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14
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0, 0, 26, 232, 1124, 3896, 10894, 26192, 56296, 110960, 204130, 355000, 589196, 940072, 1450134, 2172576, 3172944, 4530912, 6342186, 8720520, 11799860, 15736600, 20711966, 26934512, 34642744, 44107856, 55636594, 69574232
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history;
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OFFSET
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1,3
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REFERENCES
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E. Bonsdorff, K. Fabel, O. Riihimaa, Schach und Zahl, 1966, p. 51-63
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LINKS
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Table of n, a(n) for n=1..28.
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 (Karl Fabel, 1966): a(n) = n(n - 2)(2n^4 - 4n^3 + 7n^2 - 6n + 4)/12 if n is even and a(n) = (n - 1)(2n^5 - 6n^4 + 9n^3 - 11n^2 + 5n - 3)/12 if n is odd.
G.f.: -2x^3*(3x^4+18x^3+48x^2+38x+13)/((x-1)^7*(x+1)) [From Vaclav Kotesovec, Mar 25 2010]
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CROSSREFS
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A047659, A172123
Sequence in context: A159519 A110486 A098994 * A196633 A196638 A163726
Adjacent sequences: A172121 A172122 A172123 * A172125 A172126 A172127
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Jan 26 2010
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STATUS
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approved
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