# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a323864 Showing 1-1 of 1 %I A323864 #13 Aug 23 2019 11:23:33 %S A323864 1,2,4,12,32,60,216,252,912,1494,3960,4092,23904,16380,65016,130920, %T A323864 324960,262140,1569132,1048572,6281280,8388072,16769016,16777212, %U A323864 134150880,100663050,268402680,536865840,1610449344,1073741820,8589664080,4294967292,25768888320 %N A323864 Number of aperiodic binary arrays of size n. %C A323864 An n X k matrix is aperiodic if all n * k rotations of its sequence of rows and its sequence of columns are distinct. %H A323864 Andrew Howroyd, Table of n, a(n) for n = 0..200 %F A323864 a(n) = Sum_{d|n} A323860(d, n/d). - _Andrew Howroyd_, Aug 21 2019 %e A323864 The a(4) = 32 arrays: %e A323864 [0001][0010][0011][0100][0110][0111][1000][1001][1011][1100][1101][1110] %e A323864 . %e A323864 [00] [00] [01] [01] [10] [10] [11] [11] %e A323864 [01] [10] [00] [11] [00] [11] [01] [10] %e A323864 . %e A323864 [0] [0] [0] [0] [0] [0] [1] [1] [1] [1] [1] [1] %e A323864 [0] [0] [0] [1] [1] [1] [0] [0] [0] [1] [1] [1] %e A323864 [0] [1] [1] [0] [1] [1] [0] [0] [1] [0] [0] [1] %e A323864 [1] [0] [1] [0] [0] [1] [0] [1] [1] [0] [1] [0] %t A323864 apermatQ[m_]:=UnsameQ@@Join@@Table[RotateLeft[m,{i,j}],{i,Length[m]},{j,Length[First[m]]}]; %t A323864 zaz[n_]:=Join@@(Table[Partition[#,d],{d,Divisors[n]}]&/@Tuples[{0,1},n]); %t A323864 Table[Length[Select[zaz[n],apermatQ]],{n,10}] %Y A323864 Cf. A000740, A027375, A265627, A323351. %Y A323864 Cf. A323860, A323862, A323863, A323865, A323867, A323869. %K A323864 nonn %O A323864 0,2 %A A323864 _Gus Wiseman_, Feb 04 2019 %E A323864 Terms a(18) and beyond from _Andrew Howroyd_, Aug 21 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE