OFFSET
0,13
COMMENTS
T(n,k) = T(n,n-k). When 0 and 1 are switched, the number of equivalence classes remain the same.
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 A008300. 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. The number of partitions squared increases rapidly with n. For example, A000041(20)^2 = 393129. - Andrew Howroyd, Apr 03 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..189
FORMULA
Sum_{k=1..n} T(n, k) = A000519(n).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 1, 2, 1, 1;
1, 1, 2, 2, 1, 1;
1, 1, 4, 7, 4, 1, 1;
1, 1, 4, 16, 16, 4, 1, 1;
1, 1, 7, 51, 194, 51, 7, 1, 1;
1, 1, 8, 224, 3529, 3529, 224, 8, 1, 1;
...
KEYWORD
nonn,tabl
AUTHOR
Joost Vermeij (joost_vermeij(AT)live.nl), Jan 04 2008
EXTENSIONS
Missing a(72) inserted by Andrew Howroyd, Apr 01 2020
STATUS
approved