A000512 Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 3, where equivalence is defined by row and column permutations.

0, 0, 1, 1, 2, 7, 16, 51, 224, 1165, 7454, 56349, 481309, 4548786, 46829325, 519812910, 6177695783, 78190425826, 1049510787100, 14886252250208, 222442888670708, 3492326723315796, 57468395960854710, 989052970923320185, 17767732298980160822, 332572885090541084172, 6475438355244504235759, 130954580036269713385884

Offset: 1

Author

Eric Rogoyski

Keywords

• nonn
• hard

Comments

Also, isomorphism classes of bicolored cubic bipartite graphs, where isomorphism cannot exchange the colors.

Examples

			n=4: every matrix with 3 1's in each row and column can be transformed by permutation of rows (or columns) into {1110,1101,1011,0111}, therefore a(4)=1. - _Michael Steyer_, Feb 20 2003
		

References

• A. Burgess, P. Danziger, E. Mendelsohn, B. Stevens, Orthogonally Resolvable Cycle Decompositions, 2013; http://www.math.ryerson.ca/~andrea.burgess/OCD-submit.pdf
• Goulden and Jackson, Combin. Enum., Wiley, 1983 p. 284.

Links

• Index entries for sequences related to Latin squares and rectangles

Crossrefs

Column k=3 of A133687.

Cf. A000186, A000513, A000840, A001501, A008325, A232215.

A079815 may be an erroneous version of this, or it may have a slightly different (as yet unknown) definition. - N. J. A. Sloane, Sep 04 2010.

Extensions

Definition corrected by Brendan McKay, May 28 2006

a(1)-a(12) checked by Brendan McKay, Aug 27 2010

Terms a(15) and beyond from Andrew Howroyd, Apr 01 2020