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A147774 Number of equivalence classes of normalized Hadamard matrices of order 4n with respect to permutations of rows and columns.

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%I A147774 #8 Feb 16 2025 08:33:09
%S A147774 1,1,2,118,6520,43966313
%N A147774 Number of equivalence classes of normalized Hadamard matrices of order 4n with respect to permutations of rows and columns.
%C A147774 Number of equivalence classes N(k) = {1, 1, 1, 1, 2, 118, 6520, 43966313} for order k = {1, 2, 4, 8, 12, 16, 20, 24}, (see Theorem 2 at the Hadamard matrices project results link). Note that N(24) = a(6) = 43966313 is a prime.
%H A147774 <a href="http://www.chrek.ru/page.aspx?id_page=1706">Hadamard Matrices Project</a>. <a href="http://www.chrek.ru/page.aspx?id_page=1711">Results</a> (in Russian) [broken link]
%H A147774 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HadamardMatrix.html">Hadamard Matrix</a>
%Y A147774 Cf. A007299 = Number of Hadamard matrices of order 4n.
%K A147774 more,nonn
%O A147774 1,3
%A A147774 _Alexander Adamchuk_, Nov 12 2008