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A001496 Number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to n.
(Formerly M5158 N2240)
8
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of 4 X 4 stochastic matrices of integers.

REFERENCES

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.

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).

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.

LINKS

T. D. Noe, Table of n, a(n) for n=0..1000

FORMULA

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)

CROSSREFS

Cf. A002817, A003438, A019298.

Sequence in context: A007191 A097340 A222156 * A055754 A035707 A035475

Adjacent sequences:  A001493 A001494 A001495 * A001497 A001498 A001499

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vladeta Jovovic, Feb 06 2000

STATUS

approved

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Last modified June 18 19:42 EDT 2013. Contains 226356 sequences.