cp's OEIS Frontend

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.

%I A171806 #22 May 11 2020 01:38:54
%S A171806 1,25,20,30,24,20
%N 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.
%C A171806 The sum of the terms of this sequence is equal to the number of 5 X 5 permutation matrices: 5! = 120.
%C A171806 Number of elements of order n in symmetric group S_5. - _Alois P. Heinz_, Mar 30 2020
%e A171806 a(1) = 1 because there is only one matrix whose first power is the identity matrix (this is the identity matrix itself).
%t A171806 tab = {0, 0, 0, 0, 0, 0}; per =
%t A171806  Permutations[{1, 2, 3, 4, 5}]; zeromat = {}; Do[
%t A171806  AppendTo[zeromat, Table[0, {n, 1, 5}]], {m, 1, 5}]; unit =
%t A171806  IdentityMatrix[5]; s5 = {}; Do[s = zeromat;
%t A171806  Do[s[[m]][[per[[n]][[m]]]] = 1, {m, 1, 5}];
%t A171806  AppendTo[s5, s], {n, 1, 120}]; Do[
%t A171806  If[MatrixPower[s5[[n]], 1] == unit, tab[[1]] = tab[[1]] + 1,
%t A171806   If[MatrixPower[s5[[n]], 2] == unit, tab[[2]] = tab[[2]] + 1,
%t A171806    If[MatrixPower[s5[[n]], 3] == unit, tab[[3]] = tab[[3]] + 1,
%t A171806     If[MatrixPower[s5[[n]], 4] == unit, tab[[4]] = tab[[4]] + 1,
%t A171806      If[MatrixPower[s5[[n]], 5] == unit, tab[[5]] = tab[[5]] + 1,
%t A171806       If[MatrixPower[s5[[n]], 6] == unit,
%t A171806        tab[[6]] = tab[[6]] + 1]]]]]], {n, 1, 120}]; tab
%Y A171806 Row n=5 of A057731.
%K A171806 nonn,fini,full
%O A171806 1,2
%A A171806 _Artur Jasinski_, Dec 18 2009
%E A171806 Name edited and terms corrected by _Alois P. Heinz_, Mar 30 2020