cp's OEIS Frontend

A079815 Number of equivalent classes of n X n 0-1 matrices with 3 1's in each row and column.

%I A079815 #7 Dec 06 2014 17:58:59
%S A079815 0,0,1,1,2,7,16,71
%N A079815 Number of equivalent classes of n X n 0-1 matrices with 3 1's in each row and column.
%C A079815 Matrices are considered to belong to the same equivalent class if they can be transformed into each other by successive permutations of rows or columns.
%C A079815 In general, to transform 2 equivalent matrices into each other, it is necessary to first permute rows, then columns, then rows and so on.
%C A079815 From _Brendan McKay_, Aug 27 2010: (Start)
%C A079815 A079815 appears on the surface to describe the same objects as A000512, but I don't know where the term "71" comes from.
%C A079815 Also the comment "In general, to transform 2 equivalent matrices into each other, it is necessary to first permute rows, then columns, then rows and so on." is wrong - actually only one permutation of rows and one permutation of columns is enough.
%C A079815 I will guess that this sequence counts matrices in which both the rows and columns are in sorted order. The reason I suspect that is because a common way to make such matrices is to alternately sort the rows and columns until it stabilizes.
%C A079815 The value of a(8) should be checked. (End)
%e A079815 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.
%Y A079815 Cf. A001501.
%K A079815 more,nonn,obsc
%O A079815 1,5
%A A079815 Michael Steyer (m.steyer(AT)osram.de), Feb 20 2003
%E A079815 Edited by _N. J. A. Sloane_, Sep 04 2010