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

0,3

Comments

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

Links

Table of n, a(n) for n=0..20.

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.

Sequence in context: A199140 A154606 A369387 * A167143 A136732 A108239

Adjacent sequences: A232213 A232214 A232215 * A232217 A232218 A232219

Keyword

nonn

Author

N. J. A. Sloane, Nov 22 2013

Extensions

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

Status

approved