A072148 -id:A072148 - cp's OEIS frontend

A111485 Number of (-1,0,1) periodic irreducible matrices up to sign change, transposition and mirroring over the antidiagonal.

1, 3, 12, 107, 951, 10923

Offset: 1

Wouter Meeussen, Nov 15 2005

"Irreducible" is intended to mean "not factoring into blocks along the diagonal". The periods for n=6 are 396 times period 3, 2939 times period 4, 1684 times period 6 and 5904 times period 12.

Wouter Meeussen, Periodic
Eric Weisstein's World of Mathematics, Periodic Matrices

Cf. A072148.

A111749 Number of (-1,0,1) periodic irreducible matrices (with Tij = -Tji for i < j) up to sign change, transposition and row and column permutations.

Original entry on oeis.org

1, 3, 10, 39, 121, 405

Offset: 1

Wouter Meeussen, Nov 19 2005

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.

			{{-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.

Wouter Meeussen, Periodic Matrices. [broken link]

Cf. A072148, A111485.

Mathematica
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cp's OEIS Frontend

A111485 Number of (-1,0,1) periodic irreducible matrices up to sign change, transposition and mirroring over the antidiagonal.

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