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.
%I A353052 #21 Jun 14 2022 21:40:01
%S A353052 1,2,3,10,30,242,4386
%N A353052 Number of inequivalent {-1,1} matrices of order n, up to permutation of rows and/or columns, multiplication of rows and/or columns by -1, and transposition.
%C A353052 The equivalence operations described in the title are commonly used when discussing Hadamard matrices, for example (see A096201). They are natural when considering norms of these matrices or properties that can be inferred from their singular values, since they do not change singular values. See A352099 for the version of this sequence that does not consider transposition as part of the equivalence relation.
%C A353052 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*(n-2)] / (n!)^2.
%H A353052 John Holbrook, Nathaniel Johnston, and Jean-Pierre Schoch, <a href="https://arxiv.org/abs/2206.02863">Real Schur norms and Hadamard matrices</a>, arXiv:2206.02863 [math.CO], 2022.
%H A353052 Nathaniel Johnston, <a href="/A353052/a353052.txt">All inequivalent matrices of size 6-by-6 or less</a>
%e A353052 When n = 3, there are 3 inequivalent matrices, so a(3) = 3:
%e A353052 1 1 1 1 1 1 1 1 1
%e A353052 1 1 1 1 1 -1 1 -1 -1
%e A353052 1 1 1 and 1 -1 -1 and 1 -1 -1
%e A353052 All other 3-by-3 matrices with entries in {-1,1} can be converted into one of these three matrices by permutating rows and/or columns, multiplying some rows and/or columns by -1, and potentially transposing the matrix.
%Y A353052 Cf. A111368, A352099.
%K A353052 nonn,hard,more
%O A353052 1,2
%A A353052 _Nathaniel Johnston_, Apr 20 2022
%E A353052 a(7) from _Nathaniel Johnston_, May 05 2022