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

1,2

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.

Sequence in context: A107240 A099171 A268561 * A012307 A012311 A012513

Adjacent sequences: A352096 A352097 A352098 * A352100 A352101 A352102

Keyword

nonn,changed

Author

Nathaniel Johnston, May 05 2022

Extensions

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

Status

approved