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 A333737 #15 Mar 31 2025 15:21:13 %S A333737 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 A333737 1,1,1,1,4,13,33,29,11,1,1,1,1,4,20,74,142,79,15,1,1,1,1,5,28,163,556, %U A333737 742,225,22,1,1,1,1,5,39,319,1919,5369,4454,677,30,1,1 %N A333737 Array read by antidiagonals: T(n,k) is the number of non-isomorphic n X n nonnegative integer symmetric matrices with all row and column sums equal to k up to permutations of rows and columns. %C A333737 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 A188403. Burnside's lemma as applied in A318805 can be used to extend this method to the unlabeled case. %H A333737 Andrew Howroyd, <a href="/A333737/b333737.txt">Table of n, a(n) for n = 0..377</a> %H A333737 Ming Yean Lim, <a href="https://arxiv.org/abs/2503.21108">The number of irreducibles in the plethysm s_lambda[s_m]</a>, arXiv:2503.21108 [math.CO], 2025. See p. 8. %e A333737 Array begins: %e A333737 ============================================== %e A333737 n\k | 0 1 2 3 4 5 6 7 %e A333737 ----+----------------------------------------- %e A333737 0 | 1 1 1 1 1 1 1 1 ... %e A333737 1 | 1 1 1 1 1 1 1 1 ... %e A333737 2 | 1 1 2 2 3 3 4 4 ... %e A333737 3 | 1 1 3 5 9 13 20 28 ... %e A333737 4 | 1 1 5 12 33 74 163 319 ... %e A333737 5 | 1 1 7 29 142 556 1919 5793 ... %e A333737 6 | 1 1 11 79 742 5369 31781 156191 ... %e A333737 7 | 1 1 15 225 4454 64000 692599 5882230 ... %e A333737 ... %e A333737 The T(3,3) = 5 matrices are: %e A333737 [0 0 3] [0 1 2] [0 1 2] [1 0 2] [1 1 1] %e A333737 [0 3 0] [1 1 1] [1 2 0] [0 3 0] [1 1 1] %e A333737 [3 0 0] [2 1 0] [2 0 1] [2 0 1] [1 1 1] %Y A333737 Rows n=0..5 are A000012, A000012, A008619, A106607, A333886, A333887. %Y A333737 Columns n=0..5 are A000012, A000012, A000041, A333888, A333889, A333890. %Y A333737 Main diagonal is A333738. %Y A333737 Cf. A188403 (labeled case), A333159 (binary), A333733 (not necessarily symmetric). %Y A333737 Cf. A318805, A333893. %K A333737 nonn,tabl %O A333737 0,13 %A A333737 _Andrew Howroyd_, Apr 08 2020