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

Author

Eric Rogoyski

Keywords

• nonn

Examples

			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
		

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

• 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

Crossrefs

Column k=4 of A133687.

Cf. A000512.

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