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Search: id:A081623
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| A081623 |
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Number of ways in which the points on an n X n square lattice can be equally occupied with spin "up" and spin "down" particles. If n is odd, we arbitrarily take the lattice to contain one more spin "up" particle than the number of spin "down" particles. |
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1
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| 1, 6, 126, 12870, 5200300, 9075135300, 63205303218876, 1832624140942590534, 212392290424395860814420, 100891344545564193334812497256, 191645966716130525165099506263706416, 1480212998448786189993816895482588794876100
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Brian Hayes, The World in a Spin, American Scientist, vol. 88, pp. 384-388 (2000).
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LINKS
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Brian Hayes, The World in a Spin.
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FORMULA
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a(n) = C(n^2, (n^2+1)/2) if n is odd and C(n^2, n^2/2) if n is even
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EXAMPLE
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a(2)=6 because C(4,2)=6
a(3)=126 because C(9,5)=126
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PROGRAM
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(Mathcad or Microsoft Excel): f(n)=combin(n^2, trunc((n^2+1)/2))
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CROSSREFS
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Sequence in context: A109820 A004993 A133792 this_sequence A089314 A111873 A012842
Adjacent sequences: A081620 A081621 A081622 this_sequence A081624 A081625 A081626
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KEYWORD
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easy,nonn
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AUTHOR
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Tim Royappa (royappa(AT)uwf.edu), Apr 22 2003
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