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%I #31 Apr 02 2020 11:45:37
%S 0,0,0,1,1,4,16,194,3529,121790,5582612,317579783,21543414506,
%T 1711281449485,157117486414656,16502328443493967,1965612709107379155,
%U 263512349078757245789,39497131936385398782814,6579940884199010139737829,1211896874083479131415289345,245593008009270037388205883048
%N 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.
%D A. Burgess, P. Danziger, E. Mendelsohn, B. Stevens, Orthogonally Resolvable Cycle Decompositions, 2013; http://www.math.ryerson.ca/~andrea.burgess/OCD-submit.pdf
%H A. Al-Azemi, <a href="https://www.alazmi95.com/ewExternalFiles/iso_rej.pdf">Isomorph-rejection: theory and an application</a>, Kuwait J. Sci., 39 (2A) (2012), 1-14. - From _N. J. A. Sloane_, Mar 01 2013
%H A. Burgess, P. Danziger, E. Mendelsohn, B. Stevens, <a href="https://doi.org/10.1002/jcd.21404">Orthogonally Resolvable Cycle Decompositions</a>, Journal of Combinatorial Designs, Volume 23, Issue 8, August 2015, Pages 328-351.
%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%e a(4) = 1:
%e 1111
%e 1111
%e 1111
%e 1111
%e a(5)=1:
%e 01111
%e 10111
%e 11011
%e 11101
%e 11110
%e Two of the four examples with n = 6:
%e 111100 . 111100
%e 110011 . 011110
%e 001111 . 001111
%e 111100 . 100111
%e 110011 . 110011
%e 001111 . 111001
%Y Column k=4 of A133687.
%Y Cf. A000512.
%K nonn
%O 1,6
%A Eric Rogoyski
%E Definition corrected by _Brendan McKay_, May 28 2006
%E Offset corrected and a(12) added (from Al-Azemi) by _N. J. A. Sloane_, Mar 01 2013
%E Terms a(13) and beyond from _Andrew Howroyd_, Apr 01 2020
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