OFFSET
1,2
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
EXAMPLE
a(1) = 1 because there is only one matrix whose first power is the identity matrix (this is the identity matrix itself).
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
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Artur Jasinski, Dec 18 2009
EXTENSIONS
Name edited and terms corrected by Alois P. Heinz, Mar 30 2020
STATUS
approved