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%I #40 Apr 04 2020 19:05:17
%S 1,1,2,5,12,31,103,383,1731,9273,57563,406465,3212131,28009976,
%T 266688867,2749264797,30480560319,361435864747,4562860845767,
%U 61084137737436,864206301930764,12882343725953858,201788397502682460,3313420771907580764,56910480298885139055
%N Number of n X n matrices (up to permutation of their rows and columns) with nonnegative integer entries with all row and column sums equal to 3.
%C Arises from counting of symmetric tensor invariants without color. See Geloun-Ramgoolam, Section 6.2 for information and Mathematica code.
%H Mehmet Emin Aktas, <a href="https://arxiv.org/abs/1706.09956">Dessins d'Enfants of Trigonal Curves</a>, arXiv:1706.09956 [math.AG], 2017, Theorem 5.
%H J. B. Geloun, S. Ramgoolam, <a href="http://arxiv.org/abs/1307.6490">Counting Tensor Model Observables and Branched Covers of the 2-Sphere</a>, arXiv preprint arXiv:1307.6490 [hep-th], 2013.
%H Brendan McKay, <a href="http://mathoverflow.net/a/251932/11236">Number of all different n-by-n matrices where sum of rows and columns is 3</a>, MathOverflow, 2016.
%H B. D. McKay and N. C. Wormald, <a href="http://users.cecs.anu.edu.au/~bdm/papers/AutomSpecDeg.pdf">Autormorphisms of Random Graphs with Specified Vertices</a>. Combinatorica 4 (4) (1984) 325-338.
%F a(n) = 1 + Sum_{i=1..n} A328159(i). - _Brendan McKay_, Oct 05 2019
%e a(2) = 2 because there are 2 such 2 X 2 matrices: [1 2;2 1] and [3 0;0 3]. - _Nathaniel Johnston_, Oct 12 2016
%Y Column k=3 of A333733.
%Y Cf. A328159.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 22 2013
%E New name and a(9)-a(11) from _Nathaniel Johnston_, Oct 12 2016
%E a(12) and a(13) from _Brendan McKay_, Oct 05 2019
%E a(0)=1 prepended, a(12)-a(13) corrected and terms a(14) and beyond from _Andrew Howroyd_, Apr 04 2020
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