A000513 - OEIS

A000513

Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 4, where equivalence is defined by row and column permutations. Also number of isomorphism classes of bicolored quartic bipartite graphs, where isomorphism cannot exchange the colors.

0, 0, 0, 1, 1, 4, 16, 194, 3529, 121790, 5582612, 317579783, 21543414506, 1711281449485, 157117486414656, 16502328443493967, 1965612709107379155, 263512349078757245789, 39497131936385398782814, 6579940884199010139737829, 1211896874083479131415289345, 245593008009270037388205883048

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OFFSET

1,6

REFERENCES

A. Burgess, P. Danziger, E. Mendelsohn, B. Stevens, Orthogonally Resolvable Cycle Decompositions, 2013; http://www.math.ryerson.ca/~andrea.burgess/OCD-submit.pdf

LINKS

Table of n, a(n) for n=1..22.

A. Al-Azemi, Isomorph-rejection: theory and an application, Kuwait J. Sci., 39 (2A) (2012), 1-14. - From N. J. A. Sloane, Mar 01 2013

A. Burgess, P. Danziger, E. Mendelsohn, B. Stevens, Orthogonally Resolvable Cycle Decompositions, Journal of Combinatorial Designs, Volume 23, Issue 8, August 2015, Pages 328-351.

Index entries for sequences related to Latin squares and rectangles

EXAMPLE

a(4) = 1:

1111

a(5)=1:

01111

10111

11011

11101

11110

Two of the four examples with n = 6:

111100 . 111100

110011 . 011110

001111 . 001111

111100 . 100111

110011 . 110011

001111 . 111001

CROSSREFS

Column k=4 of A133687.

Cf. A000512.

Sequence in context: A280468 A366818 A224802 * A088027 A271267 A333438

Adjacent sequences: A000510 A000511 A000512 * A000514 A000515 A000516

KEYWORD

nonn

AUTHOR

Eric Rogoyski

EXTENSIONS

Definition corrected by Brendan McKay, May 28 2006

Offset corrected and a(12) added (from Al-Azemi) by N. J. A. Sloane, Mar 01 2013

Terms a(13) and beyond from Andrew Howroyd, Apr 01 2020

STATUS

approved