OFFSET
0,4
COMMENTS
The 1-dimensional case is A000740.
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 = 0..200
EXAMPLE
The a(5) = 33 arrays:
5 14 23 32 41 113 122 131 212 221 311 1112 1121 1211 2111
.
1 2 3 4 11 11 12 21
4 3 2 1 12 21 11 11
.
1 1 1 2 2 3
1 2 3 1 2 1
3 2 1 2 1 1
.
1 1 1 2
1 1 2 1
1 2 1 1
2 1 1 1
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
ptnmats[n_]:=Union@@Permutations/@Select[Union@@(Tuples[Permutations/@#]&/@Map[primeMS, facs[n], {2}]), SameQ@@Length/@#&];
apermatQ[m_]:=UnsameQ@@Join@@Table[RotateLeft[m, {i, j}], {i, Length[m]}, {j, Length[First[m]]}];
Table[Length[Union@@Table[Select[ptnmats[k], apermatQ], {k, Times@@Prime/@#&/@IntegerPartitions[n]}]], {n, 15}]
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 04 2019
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Aug 21 2019
STATUS
approved