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 A333901. Burnside's lemma can be used to extend this method to the unlabeled case. This seems to require looping over partitions for both rows and columns.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..324 (first 25 antidiagonals)
FORMULA
T(n,k) = T(k,n).
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 2 5 9 14 28 44 ...
4 | 1 1 3 9 43 147 661 2649 ...
5 | 1 1 3 14 147 1856 25888 346691 ...
6 | 1 1 4 28 661 25888 1217727 55138002 ...
7 | 1 1 4 44 2649 346691 55138002 8597641912 ...
...
CROSSREFS
KEYWORD
AUTHOR
Andrew Howroyd, Oct 14 2024
STATUS
approved