A171809 Number of 5 X 5 permutation matrices such that the n-th matrix power is the identity matrix and the determinant is -1.
0, 10, 0, 30, 0, 20
Offset: 1
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a(0)=44 because we have 44 different permutation matrices 5 x 5 with trace 0.
a(0)=24 because we have 24 different permutation matrices 5 x 5 with trace 0 and determinant +1.
a(0)=20 because we have 20 different permutation matrices 5 x 5 with trace 0 and determinant -1.