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A036464
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Number of ways to place two nonattacking queens on an n X n board.
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13
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0, 0, 8, 44, 140, 340, 700, 1288, 2184, 3480, 5280, 7700, 10868, 14924, 20020, 26320, 34000, 43248, 54264, 67260, 82460, 100100, 120428, 143704, 170200, 200200, 234000, 271908, 314244, 361340, 413540, 471200, 534688, 604384
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OFFSET
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1,3
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REFERENCES
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S. Chaiken, C. R. H. Hanusa and T. Zaslavsky, A q-queens problem I. General theory, January 26, 2013; http://www.math.binghamton.edu/zaslav/Tpapers/qq1.pdf. - From N. J. A. Sloane, Feb 16 2013
I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math. Monthly, 101 (1994), 629-639.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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a(n) = C(n, 3)*(3*n-1).
G.f.: 4*x^3*(2+x)/(1-x)^5. [Colin Barker, May 02 2012]
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MAPLE
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f:=n->n^4/2 - 5*n^3/3 + 3*n^2/2 - n/3; [seq(f(n), n=1..200)]; # From N. J. A. Sloane, Feb 16 2013
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MATHEMATICA
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f[k_] := 2 k; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 50}] (* A036464 *)
Table[a[n]/4, {n, 2, 50}] (* A000914 *)
(* Clark Kimberling, Dec 31 2011 *)
CoefficientList[Series[4 x^2 (2 + x) / (1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, May 02 2013 *)
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CROSSREFS
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Sequence in context: A075816 A188148 A100583 * A000938 A165618 A059596
Adjacent sequences: A036461 A036462 A036463 * A036465 A036466 A036467
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Robert G. Wilson v, Raymond Bush (c17h21no4(AT)hotmail.com), Kirk Conely, N. J. A. Sloane.
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STATUS
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approved
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