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A232215
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.
3
1, 1, 2, 5, 12, 31, 103, 383, 1731, 9273, 57563, 406465, 3212131, 28009976, 266688867, 2749264797, 30480560319, 361435864747, 4562860845767, 61084137737436, 864206301930764, 12882343725953858, 201788397502682460, 3313420771907580764, 56910480298885139055
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
Mehmet Emin Aktas, Dessins d'Enfants of Trigonal Curves, arXiv:1706.09956 [math.AG], 2017, Theorem 5.
J. B. Geloun, S. Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere, arXiv preprint arXiv:1307.6490 [hep-th], 2013.
B. D. McKay and N. C. Wormald, Autormorphisms of Random Graphs with Specified Vertices. Combinatorica 4 (4) (1984) 325-338.
FORMULA
a(n) = 1 + Sum_{i=1..n} A328159(i). - Brendan McKay, Oct 05 2019
EXAMPLE
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
CROSSREFS
Column k=3 of A333733.
Cf. A328159.
Sequence in context: A132441 A000840 A362635 * A265265 A293868 A162434
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 22 2013
EXTENSIONS
New name and a(9)-a(11) from Nathaniel Johnston, Oct 12 2016
a(12) and a(13) from Brendan McKay, Oct 05 2019
a(0)=1 prepended, a(12)-a(13) corrected and terms a(14) and beyond from Andrew Howroyd, Apr 04 2020
STATUS
approved