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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 (list; graph; refs; listen; history; text; internal format)
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..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 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.

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

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)