A352099 Number of inequivalent {-1,1} matrices of order n, up to permutation of rows and/or columns and multiplication of rows and/or columns by -1.

1, 2, 3, 12, 39, 388, 8102, 656108, 199727714, 224693292768, 893966897828288, 12397352268917562436, 598097093939369977901540, 100707091308314174859433507948, 59497535893138933753768955970555554, 124081719421265185713331815803874814236572, 919072633264334061873768956083917736204779032768

Offset: 1

Author

Nathaniel Johnston, May 05 2022

Keywords

• nonn

Comments

The equivalence operations described in the title are commonly used when discussing Hadamard matrices, for example (see A007299). See A353052 for the version of this sequence that also considers transposition as part of the equivalence relation.

Since the row and column multiplication operations can be used to force the first row and column to consist only of ones, 2^((n-1)^2) is an upper bound on this sequence. A lower bound is 2^((n-1)^2) / (n!)^2.

Links

• Eugene Nonko, Table of n, a(n) for n = 1..45
• Project Euler, Problem 626: Counting Binary Matrices.

Crossrefs

Cf. A007299, A111368, A353052.

Extensions

a(8) onwards from Eugene Nonko, Nov 30 2024