

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.


9



0, 0, 1, 1, 2, 7, 16, 51, 224, 1165, 7454, 56349, 481309, 4548786
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OFFSET

1,5


COMMENTS

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


REFERENCES

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


LINKS

Table of n, a(n) for n=1..14.
Index entries for sequences related to Latin squares and rectangles


EXAMPLE

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 (m.steyer(AT)osram.de), Feb 20 2003


CROSSREFS

Cf. A000186, A000513, A001501.
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.
Sequence in context: A248114 A330227 A322192 * A084079 A286848 A239425
Adjacent sequences: A000509 A000510 A000511 * A000513 A000514 A000515


KEYWORD

nonn,hard,more


AUTHOR

Eric Rogoyski


EXTENSIONS

Definition corrected by Brendan McKay, May 28 2006
a(1)a(12) checked by Brendan McKay, Aug 27 2010


STATUS

approved



