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

1,5

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/OCD-submit.pdf

Goulden and Jackson, Combin. Enum., Wiley, 1983 p. 284.

Links

Table of n, a(n) for n=1..28.

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, Feb 20 2003

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.

Sequence in context: A248114 A330227 A322192 * A084079 A286848 A239425

Adjacent sequences: A000509 A000510 A000511 * A000513 A000514 A000515

Keyword

nonn,hard

Author

Eric Rogoyski

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

Status

approved