OFFSET
1,2
COMMENTS
An n X k matrix is aperiodic if all n * k rotations of its sequence of rows and its sequence of columns are distinct.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
a(n) = n*A323871(n). - Andrew Howroyd, Aug 21 2019
EXAMPLE
The a(3) = 24 matrices:
[123][132][213][312][231][321][122][211][112][221][121][212]
.
[1][1][2][3][2][3][1][2][1][2][1][2]
[2][3][1][1][3][2][2][1][1][2][2][1]
[3][2][3][2][1][1][2][1][2][1][1][2]
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
nrmmats[n_]:=Join@@Table[Table[Table[Position[stn, {i, j}][[1, 1]], {i, d}, {j, n/d}], {stn, Join@@Permutations/@sps[Tuples[{Range[d], Range[n/d]}]]}], {d, Divisors[n]}];
apermatQ[m_]:=UnsameQ@@Join@@Table[RotateLeft[m, {i, j}], {i, Length[m]}, {j, Length[First[m]]}];
Table[Length[Select[nrmmats[n], apermatQ]], {n, 6}]
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 04 2019
EXTENSIONS
Terms a(9) and beyond from Andrew Howroyd, Aug 21 2019
STATUS
approved