OFFSET
0,2
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 = 0..200
FORMULA
a(n) = Sum_{d|n} A323860(d, n/d). - Andrew Howroyd, Aug 21 2019
EXAMPLE
The a(4) = 32 arrays:
[0001][0010][0011][0100][0110][0111][1000][1001][1011][1100][1101][1110]
.
[00] [00] [01] [01] [10] [10] [11] [11]
[01] [10] [00] [11] [00] [11] [01] [10]
.
[0] [0] [0] [0] [0] [0] [1] [1] [1] [1] [1] [1]
[0] [0] [0] [1] [1] [1] [0] [0] [0] [1] [1] [1]
[0] [1] [1] [0] [1] [1] [0] [0] [1] [0] [0] [1]
[1] [0] [1] [0] [0] [1] [0] [1] [1] [0] [1] [0]
MATHEMATICA
apermatQ[m_]:=UnsameQ@@Join@@Table[RotateLeft[m, {i, j}], {i, Length[m]}, {j, Length[First[m]]}];
zaz[n_]:=Join@@(Table[Partition[#, d], {d, Divisors[n]}]&/@Tuples[{0, 1}, n]);
Table[Length[Select[zaz[n], apermatQ]], {n, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 04 2019
EXTENSIONS
Terms a(18) and beyond from Andrew Howroyd, Aug 21 2019
STATUS
approved