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Number of (-1,0,1) periodic irreducible matrices (with Tij = -Tji for i < j) up to sign change, transposition and row and column permutations.
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%I #9 May 01 2024 09:00:46

%S 1,3,10,39,121,405

%N Number of (-1,0,1) periodic irreducible matrices (with Tij = -Tji for i < j) up to sign change, transposition and row and column permutations.

%C The permutations of rows i and j, followed by those of column i and j, preserve the property that (Tij = -Tji for i < j). The periods of the 405 6 X 6 matrices are: 11 times period 3, 94 times period 4, 71 times period 6 and 229 times period 12.

%H Wouter Meeussen, <a href="http://users.pandora.be/Wouter.Meeussen/PseudoAntiSymmetricMatrixPowers.nb">Periodic Matrices</a>.

%e {{-1,-1,0,0,0,0}, {1,1,-1,0,0,0}, {0,1,-1,0,0,0}, {0,0,0,-1,-1,0}, {0,0,0,1,1,-1}, {0,0,0,0,1,-1}} is one of the 6 X 6 matrices.

%t See link.

%Y Cf. A072148, A111485.

%K nonn,hard,more

%O 1,2

%A _Wouter Meeussen_, Nov 19 2005