A003439 Number of 6 X 6 stochastic matrices of integers: all rows and columns sum to n. (Formerly M5474)

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

Offset

0,2

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]

Formula

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

Crossrefs

Row n=6 of A257493.

Cf. A005467.

Sequence in context: A008411 A221436 A239184 * A222158 A145093 A221621

Adjacent sequences: A003436 A003437 A003438 * A003440 A003441 A003442

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved