A058392
Number of 6 X 6 matrices with nonnegative integer entries and all row sums equal to n, up to row and column permutation.
Original entry on oeis.org
1, 11, 782, 96073, 9283247, 537001197, 19578605324, 487615778173, 8892272235593, 125319645293555, 1423054983691408, 13451239365449764, 108603794657349271, 764673059329865921, 4775254548845993462, 26820549989969591853, 137072193873357150230, 643738505766475169048
Offset: 0
A003439
Number of 6 X 6 stochastic matrices of integers: all rows and columns sum to n.
Original entry on oeis.org
1, 720, 202410, 20933840, 1047649905, 30767936616, 602351808741, 8575979362560, 94459713879600, 842286559093240, 6292583664553881, 40447642842118656, 228438173705550566, 1152877640765297760, 5271278793334883190, 22085628572718605376, 85604721304213863531
Offset: 0
- 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).
- 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]
More terms from Melissa Erdmann (merdmann(AT)nebrwesleyan.edu), May 07 2009
A005466
5 X 5 stochastic matrices of integers.
Original entry on oeis.org
1, 115, 5390, 101275, 858650, 3309025, 4718075
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- 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.
- I. J. Good, On the application of symmetric Dirichlet distributions and their mixtures to contingency tables, Ann. Statist. 4 (1976), no. 6, 1159-1189.
- I. J. Good, On the application of symmetric Dirichlet distributions and contingency tables, pp. 1178-1179. (Annotated scanned copy)
- 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]
A259473
Irregular triangle read by rows of coefficients arising in the enumeration of doubly stochastic matrices of integers, n >= 1, 0 <= k <= (n-1)*(n-2).
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 14, 87, 148, 87, 14, 1, 1, 103, 4306, 63110, 388615, 1115068, 1575669, 1115068, 388615, 63110, 4306, 103, 1, 1, 694, 184015, 15902580, 567296265, 9816969306, 91422589980, 490333468494, 1583419977390, 3166404385990, 3982599815746, 3166404385990
Offset: 1
Triangle begins:
1;
1;
1,1,1;
1,14,87,148,87,14,1;
1,103,4306,63110,388615,1115068,1575669,1115068,388615,63110,4306,103,1;
...
- Andrew Howroyd, Table of n, a(n) for n = 1..177 (rows 1..9)
- 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, doi:10.1137/0204040.
- 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)
a(1)=1 prepended and terms a(26) and beyond from
Andrew Howroyd, Apr 11 2020
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