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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. 5
1, 25, 20, 30, 24, 20 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=1..6.

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

Row n=5 of A057731.

Sequence in context: A104790 A291429 A334562 * A038822 A061438 A022981

Adjacent sequences:  A171803 A171804 A171805 * A171807 A171808 A171809

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

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Last modified June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)