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A333733
Array read by antidiagonals: T(n,k) is the number of non-isomorphic n X n nonnegative integer matrices with all row and column sums equal to k up to permutations of rows and columns.
11
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 3, 5, 5, 1, 1, 1, 1, 3, 9, 12, 7, 1, 1, 1, 1, 4, 13, 43, 31, 11, 1, 1, 1, 1, 4, 22, 106, 264, 103, 15, 1, 1, 1, 1, 5, 30, 321, 1856, 2804, 383, 22, 1, 1, 1, 1, 5, 45, 787, 12703, 65481, 44524, 1731, 30, 1, 1
OFFSET
0,13
COMMENTS
Terms may be computed without generating each matrix by enumerating the number of matrices by column sum sequence using dynamic programming. A PARI program showing this technique for the labeled case is given in A257493. Burnside's lemma can be used to extend this method to the unlabeled case.
EXAMPLE
Array begins:
=======================================================
n\k | 0 1 2 3 4 5 6 7
----+--------------------------------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 1 1 ...
2 | 1 1 2 2 3 3 4 4 ...
3 | 1 1 3 5 9 13 22 30 ...
4 | 1 1 5 12 43 106 321 787 ...
5 | 1 1 7 31 264 1856 12703 71457 ...
6 | 1 1 11 103 2804 65481 1217727 16925049 ...
7 | 1 1 15 383 44524 3925518 224549073 8597641912 ...
...
CROSSREFS
Columns k=0..5 are A000012, A000012, A000041, A232215, A232216, A333736.
Main diagonal is A333734.
Sequence in context: A332649 A321724 A333737 * A303929 A303694 A194673
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 04 2020
STATUS
approved