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

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
1111
1111
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