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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
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891.
C. Domb, On the theory of cooperative phenomena in crystals, Advances in Phys., 9 (1960), 149-361.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for sequences related to f.c.c. lattice
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FORMULA
| G.f.: hypergeom([1/6, 1/3],[1],108*x^2*(4*x+1))^2 - Mark van Hoeij, Oct 29 2011.
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MATHEMATICA
| f[n_] := Sum[ Binomial[n, k]*(-4)^(n - k)*Sum[ Binomial[k, j]^2*Binomial[2k - 2j, k - j]*Binomial[2j, j], {j, 0, k}], {k, 0, n}]; Array[f, 20, 0]
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PROG
| (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
| Cf. A002895.
Sequence in context: A061148 A052601 A003498 * A077612 A041272 A022282
Adjacent sequences: A002896 A002897 A002898 * A002900 A002901 A002902
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KEYWORD
| nonn,walk,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David Broadhurst (D.Broadhurst(AT)open.ac.uk), Feb 06 2008
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