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.

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

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.

Examples

			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
		

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.
• Brendan McKay, Number of all different n-by-n matrices where sum of rows and columns is 3, MathOverflow, 2016.
• B. D. McKay and N. C. Wormald, Autormorphisms of Random Graphs with Specified Vertices. Combinatorica 4 (4) (1984) 325-338.

Crossrefs

Column k=3 of A333733.

Cf. A328159.

Formula

a(n) = 1 + Sum_{i=1..n} A328159(i). - Brendan McKay, Oct 05 2019

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