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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

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

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Author

Nathaniel Johnston, May 05 2022

Keywords

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

Crossrefs

Cf. A007299, A111368, A353052.

Extensions

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