This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333733 #12 Oct 15 2024 00:03:06 %S A333733 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, %T A333733 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, %U A333733 1856,2804,383,22,1,1,1,1,5,45,787,12703,65481,44524,1731,30,1,1 %N 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. %C A333733 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. %H A333733 Andrew Howroyd, <a href="/A333733/b333733.txt">Table of n, a(n) for n = 0..275</a> (first 23 antidiagonals) %e A333733 Array begins: %e A333733 ======================================================= %e A333733 n\k | 0 1 2 3 4 5 6 7 %e A333733 ----+-------------------------------------------------- %e A333733 0 | 1 1 1 1 1 1 1 1 ... %e A333733 1 | 1 1 1 1 1 1 1 1 ... %e A333733 2 | 1 1 2 2 3 3 4 4 ... %e A333733 3 | 1 1 3 5 9 13 22 30 ... %e A333733 4 | 1 1 5 12 43 106 321 787 ... %e A333733 5 | 1 1 7 31 264 1856 12703 71457 ... %e A333733 6 | 1 1 11 103 2804 65481 1217727 16925049 ... %e A333733 7 | 1 1 15 383 44524 3925518 224549073 8597641912 ... %e A333733 ... %Y A333733 Rows n=0..5 are A000012, A000012, A008619, A052282, A052280, A333735. %Y A333733 Columns k=0..5 are A000012, A000012, A000041, A232215, A232216, A333736. %Y A333733 Main diagonal is A333734. %Y A333733 Cf. A133687, A167625, A257493, A333330, A377060. %K A333733 nonn,tabl %O A333733 0,13 %A A333733 _Andrew Howroyd_, Apr 04 2020