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 A377060 #12 Oct 15 2024 00:02:04 %S A377060 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,3,5,3,1,1,1,1,3,9,9,3, %T A377060 1,1,1,1,4,14,43,14,4,1,1,1,1,4,28,147,147,28,4,1,1,1,1,5,44,661,1856, %U A377060 661,44,5,1,1,1,1,5,73,2649,25888,25888,2649,73,5,1,1 %N A377060 Array read by antidiagonals: T(n,k) is the number of inequivalent n X k nonnegative integer matrices with all column sums n and row sums k up to permutation of rows and columns. %C A377060 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. %H A377060 Andrew Howroyd, <a href="/A377060/b377060.txt">Table of n, a(n) for n = 0..324</a> (first 25 antidiagonals) %F A377060 T(n,k) = T(k,n). %e A377060 Array begins: %e A377060 ================================================== %e A377060 n\k | 0 1 2 3 4 5 6 7 ... %e A377060 ----+--------------------------------------------- %e A377060 0 | 1 1 1 1 1 1 1 1 ... %e A377060 1 | 1 1 1 1 1 1 1 1 ... %e A377060 2 | 1 1 2 2 3 3 4 4 ... %e A377060 3 | 1 1 2 5 9 14 28 44 ... %e A377060 4 | 1 1 3 9 43 147 661 2649 ... %e A377060 5 | 1 1 3 14 147 1856 25888 346691 ... %e A377060 6 | 1 1 4 28 661 25888 1217727 55138002 ... %e A377060 7 | 1 1 4 44 2649 346691 55138002 8597641912 ... %e A377060 ... %Y A377060 Main diagonal is A333734. %Y A377060 Columns k=0..4 are A000012, A000012, A008619, A377061, A377062. %Y A377060 Cf. A333733, A333901, A377007. %K A377060 nonn,tabl %O A377060 0,13 %A A377060 _Andrew Howroyd_, Oct 14 2024