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Search: id:A002899
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| A002899 |
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Number of n-step polygons on f.c.c. lattice.
(Formerly M4840 N2068)
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+0
1
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| 1, 0, 12, 48, 540, 4320, 42240, 403200, 4038300, 40958400, 423550512, 4434978240, 46982827584, 502437551616, 5417597053440, 58831951546368, 642874989479580, 7063600894137216, 77991775777488144, 864910651813116480
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = number of 2-by-n matrices with entries from {1,2,3,4}, with (1) second row a (multiset) permutation of the first, and (2) no constant columns. [From David Callan (callan(AT)stat.wisc.edu), Aug 25 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
C. Domb, On the theory of cooperative phenomena in crystals, Advances in Phys., 9 (1960), 149-361.
David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891.
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LINKS
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Index entries for sequences related to f.c.c. lattice
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)*(-4)^(n-k)*sum(j=0, k, binomial(k, j)^2*binomial(2*k-2*j, k-j)*binomial(2*j, j)))} print(vector(20, n, a(n-1))) - David Broadhurst (D.Broadhurst(AT)open.ac.uk), Feb 06 2008
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CROSSREFS
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Cf. A002895.
Adjacent sequences: A002896 A002897 A002898 this_sequence A002900 A002901 A002902
Sequence in context: A061148 A052601 A003498 this_sequence A077612 A041272 A022282
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KEYWORD
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nonn,walk,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from David Broadhurst (D.Broadhurst(AT)open.ac.uk), Feb 06 2008
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