A232216 Number of non-isomorphic n X n nonnegative integer matrices with all row and column sums equal to 4 up to permutations of rows and columns.

1, 1, 3, 9, 43, 264, 2804, 44524, 1012456, 30502320, 1166185222, 54902972542, 3115560948081, 209575881782122, 16484822517084705, 1498893370236782629, 155996155818460127750, 18424063865105027559797, 2450806855748517847761175, 364738110721163795332103692, 60368334488355648041244493885

Offset: 0

Author

N. J. A. Sloane, Nov 22 2013

Keywords

• nonn

Comments

Arises from counting of symmetric tensor invariants without color. See Geloun-Ramgoolam, Section 6.2 for information and Mathematica code.

Links

• Erick Castro, Itzhak Roditi, A combinatorial matrix approach for the generation of vacuum Feynman graphs multiplicities in phi-4 theory, arXiv:1804.08031 [math-ph], 2018.
• J. B. Geloun, S. Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere, arXiv preprint arXiv:1307.6490 [hep-th], 2013.

Crossrefs

Column k=4 of A333733.

Extensions

Name changed, a(0)=1 prepended and a(9)-a(20) from Andrew Howroyd, Apr 04 2020