A171806 Number of 5 X 5 permutation matrices such that the n-th matrix power is the least nonnegative power that gives the identity matrix.

1, 25, 20, 30, 24, 20

Offset: 1

Author

Artur Jasinski, Dec 18 2009

Keywords

• nonn
• fini
• full

Comments

The sum of the terms of this sequence is equal to the number of 5 X 5 permutation matrices: 5! = 120.

Number of elements of order n in symmetric group S_5. - Alois P. Heinz, Mar 30 2020

Examples

			a(1) = 1 because there is only one matrix whose first power is the identity matrix (this is the identity matrix itself).
		

Crossrefs

Row n=5 of A057731.

Programs

Mathematica

tab = {0, 0, 0, 0, 0, 0}; per =
 Permutations[{1, 2, 3, 4, 5}]; zeromat = {}; Do[
 AppendTo[zeromat, Table[0, {n, 1, 5}]], {m, 1, 5}]; unit =
 IdentityMatrix[5]; s5 = {}; Do[s = zeromat;
 Do[s[[m]][[per[[n]][[m]]]] = 1, {m, 1, 5}];
 AppendTo[s5, s], {n, 1, 120}]; Do[
 If[MatrixPower[s5[[n]], 1] == unit, tab[[1]] = tab[[1]] + 1,
  If[MatrixPower[s5[[n]], 2] == unit, tab[[2]] = tab[[2]] + 1,
   If[MatrixPower[s5[[n]], 3] == unit, tab[[3]] = tab[[3]] + 1,
    If[MatrixPower[s5[[n]], 4] == unit, tab[[4]] = tab[[4]] + 1,
     If[MatrixPower[s5[[n]], 5] == unit, tab[[5]] = tab[[5]] + 1,
      If[MatrixPower[s5[[n]], 6] == unit,
       tab[[6]] = tab[[6]] + 1]]]]]], {n, 1, 120}]; tab

Extensions

Name edited and terms corrected by Alois P. Heinz, Mar 30 2020