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A000512
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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.
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11
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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
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OFFSET
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1,5
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COMMENTS
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Also, isomorphism classes of bicolored cubic bipartite graphs, where isomorphism cannot exchange the colors.
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REFERENCES
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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.
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LINKS
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EXAMPLE
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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
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CROSSREFS
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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.
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KEYWORD
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nonn,hard
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AUTHOR
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Eric Rogoyski
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EXTENSIONS
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STATUS
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approved
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