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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.
1
1, 2, 3, 12, 39, 388, 8102
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.
CROSSREFS
Sequence in context: A107240 A099171 A268561 * A012307 A012311 A012513
KEYWORD
nonn,hard,more
AUTHOR
Nathaniel Johnston, May 05 2022
STATUS
approved