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%I #22 Apr 04 2020 11:04:33
%S 0,0,1,1,2,7,16,51,224,1165,7454,56349,481309,4548786,46829325,
%T 519812910,6177695783,78190425826,1049510787100,14886252250208,
%U 222442888670708,3492326723315796,57468395960854710,989052970923320185,17767732298980160822,332572885090541084172,6475438355244504235759,130954580036269713385884
%N 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.
%C Also, isomorphism classes of bicolored cubic 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
%D Goulden and Jackson, Combin. Enum., Wiley, 1983 p. 284.
%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%e 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
%Y Column k=3 of A133687.
%Y Cf. A000186, A000513, A000840, A001501, A008325, A232215.
%Y 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.
%K nonn,hard
%O 1,5
%A Eric Rogoyski
%E Definition corrected by _Brendan McKay_, May 28 2006
%E a(1)-a(12) checked by _Brendan McKay_, Aug 27 2010
%E Terms a(15) and beyond from _Andrew Howroyd_, Apr 01 2020
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