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

0, 0, 1, 1, 2, 7, 16, 71

Offset

1,5

Comments

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.

In general, to transform 2 equivalent matrices into each other, it is necessary to first permute rows, then columns, then rows and so on.

From Brendan McKay, Aug 27 2010: (Start)

A079815 appears on the surface to describe the same objects as A000512, but I don't know where the term "71" comes from.

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.

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.

The value of a(8) should be checked. (End)

Links

Table of n, a(n) for n=1..8.

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.

Crossrefs

Cf. A001501.

Sequence in context: A042689 A073998 A129444 * A362760 A325510 A347601

Adjacent sequences: A079812 A079813 A079814 * A079816 A079817 A079818

Keyword

more,nonn,obsc

Author

Michael Steyer (m.steyer(AT)osram.de), Feb 20 2003

Extensions

Edited by N. J. A. Sloane, Sep 04 2010

Status

approved