A003439 Number of 6 X 6 stochastic matrices of integers: all rows and columns sum to n.

1, 720, 202410, 20933840, 1047649905, 30767936616, 602351808741, 8575979362560, 94459713879600, 842286559093240, 6292583664553881, 40447642842118656, 228438173705550566, 1152877640765297760, 5271278793334883190, 22085628572718605376, 85604721304213863531

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• Matthias Beck and Dennis Pixton, The Ehrhart Polynomial of the Birkhoff Polytope, Discrete & Computational Geometry, 30(4)(2003), 623-637.
• 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 and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• D. M. Jackson & G. H. J. van Rees, The enumeration of generalized double stochastic nonnegative integer square matrices, SIAM J. Comput., 4.4 (1975), 474-477. (Annotated scanned copy)
• Dennis Pixton, Ehrhart polynomials for n = 1, ..., 9
• 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. [Annotated scanned copy]

Crossrefs

Row n=6 of A257493.

Cf. A005467.

Formula

a(n) = Sum_{j=0..10} A005467(j) * binomial(5+j+n, 5+2*j). - Andrew Howroyd, Apr 09 2020

Extensions

More terms from Melissa Erdmann (merdmann(AT)nebrwesleyan.edu), May 07 2009

Offset changed to 0 by Alois P. Heinz, Apr 26 2015

Name clarified by Charles R Greathouse IV, Mar 03 2018