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Search: id:A001496
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| A001496 |
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Number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to n.
(Formerly M5158 N2240)
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+0
8
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| 1, 24, 282, 2008, 10147, 40176, 132724, 381424, 981541, 2309384, 5045326, 10356424, 20158151, 37478624, 66952936, 115479776, 193077449, 313981688, 498033282, 772409528, 1173759851, 1750812624, 2567527260, 3706873040
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of 4 X 4 stochastic matrices of integers.
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REFERENCES
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A. G. Bell, Partitioning integers in n dimensions, The Computer Journal, 13 (1970), 278-283.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 124, #25, Q(4,r).
I. J. Good, On the application of symmetric Dirichlet distributions and their mixtures to contingency tables. Ann. Statist. 4 (1976), no. 6, 1159-1189.
D. M. Jackson and G. H. J. van Rees, The enumeration of generalized double stochastic nonnegative integer square matrices, SIAM J. Comput., 4 (1975), 474-477.
R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, pages 233-234.
M. L. Stein and P. R. Stein, Enumeration of Stochastic Matrices with Integer Elements. Report LA-4434, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Jun 1970.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
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G.f.: (1+14*x+87*x^2+148*x^3+87*x^4+14*x^5+x^6)/(1-x)^10.
binomial(n + 3, 3) + 20*binomial(n + 4, 5) + 152*binomial(n + 5, 7) + 352*binomial(n + 6, 9)
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CROSSREFS
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Cf. A002817, A003438, A019298.
Sequence in context: A014809 A007191 A097340 this_sequence A055754 A035707 A035475
Adjacent sequences: A001493 A001494 A001495 this_sequence A001497 A001498 A001499
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 06 2000
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