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A172123
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Number of ways to place 2 nonattacking bishops on an n X n board.
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17
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0, 4, 26, 92, 240, 520, 994, 1736, 2832, 4380, 6490, 9284, 12896, 17472, 23170, 30160, 38624, 48756, 60762, 74860, 91280, 110264, 132066, 156952, 185200, 217100, 252954, 293076, 337792, 387440, 442370, 502944, 569536, 642532
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OFFSET
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1,2
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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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FORMULA
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a(n) = n*(n - 1)*(3*n^2 - n + 2)/6.
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Vincenzo Librandi, Apr 29 2013
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MATHEMATICA
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CoefficientList[Series[-2 x (x+1)(x+2)/(x-1)^5, {x, 0, 80}], x] (* Vincenzo Librandi, Apr 29 2013 *)
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PROG
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(Magma) [n*(n-1)*(3*n^2-n+2)/6: n in [1..40]]; /* or */ I:=[0, 4, 26, 92, 240]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Apr 29 2013
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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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