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A172141
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Number of ways to place 2 nonattacking nightriders on an n X n board.
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8
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0, 6, 28, 96, 240, 518, 980, 1712, 2784, 4310, 6380, 9136, 12688, 17206, 22820, 29728, 38080, 48102, 59964, 73920, 90160, 108966, 130548, 155216, 183200, 214838, 250380, 290192, 334544, 383830, 438340, 498496, 564608, 637126
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OFFSET
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1,2
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COMMENTS
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A nightrider is a fairy chess piece that can move (proportionate to how a knight moves) in any direction.
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REFERENCES
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Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p.829
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016
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 (Christian Poisson, 1990): a(n) = n(3n^3 - 5n^2 + 9n - 4)/6 if n is even and a(n) = n(n - 1)(3n^2 - 2n + 7)/6 if n is odd.
G.f.: -2x^2*(x^2+2x+3)(2x^2+x+1)/((x-1)^5*(x+1)^2) [From Vaclav Kotesovec, Mar 25 2010]
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MATHEMATICA
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CoefficientList[Series[-2 x (x^2 + 2 x + 3) (2 x^2 + x + 1) / ((x - 1)^5 (x + 1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)
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CROSSREFS
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A036464, A172123, A172132, A172137.
Sequence in context: A091321 A125310 A138874 * A172132 A011856 A276041
Adjacent sequences: A172138 A172139 A172140 * A172142 A172143 A172144
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KEYWORD
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easy,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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