

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
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OFFSET

0,3


COMMENTS

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


LINKS

Table of n, a(n) for n=0..24.
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 2Sphere, arXiv preprint arXiv:1307.6490 [hepth], 2013.
Brendan McKay, Number of all different nbyn 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) 325338.


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: A090826 A132441 A000840 * A265265 A293868 A162434
Adjacent sequences: A232212 A232213 A232214 * A232216 A232217 A232218


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



