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a(n) is the number of symmetric anti-Hadamard matrices of order n whose sum of the inverse squares of their singular values is maximal.
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%I #8 Mar 13 2022 18:56:39

%S 1,2,6,24,120,840,5040

%N a(n) is the number of symmetric anti-Hadamard matrices of order n whose sum of the inverse squares of their singular values is maximal.

%C The sequence of the ratio a(n+1)/a(n) begins with 2, 3, 4, 5, 7, 6, ...

%C Is a(n+1)/a(n) integer for all n? If that is true, excluding the number 1, is the sequence of the ratio a(n+1)/a(n) a permutation of all other natural numbers?

%H R. L. Graham and N. J. A. Sloane, <a href="http://dx.doi.org/10.1016/0024-3795(84)90090-9">Anti-Hadamard matrices</a>, Linear Alg. Applic., 62 (1984), 113-137.

%Y Cf. A005312, A005313, A119002, A351153.

%K nonn,hard,more

%O 1,2

%A _Stefano Spezia_, Feb 27 2022