cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A323863 Number of n X n aperiodic binary arrays.

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%I A323863 #15 Aug 22 2019 20:47:36
%S A323863 1,2,8,486,64800,33554250,68718675672,562949953420302,
%T A323863 18446744060824780800,2417851639229257812542976,
%U A323863 1267650600228226023797043513000,2658455991569831745807614120560664598,22300745198530623141521551172073990303938400
%N A323863 Number of n X n aperiodic binary arrays.
%C A323863 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 A323863 Andrew Howroyd, <a href="/A323863/b323863.txt">Table of n, a(n) for n = 0..50</a>
%F A323863 a(n) = 2^(n^2) - (n+1)*2^n + 2*n if n is prime. - _Robert Israel_, Feb 04 2019
%F A323863 a(n) = n^2 * A323872(n). - _Andrew Howroyd_, Aug 21 2019
%e A323863 The a(2) = 8 arrays are:
%e A323863   [0 0] [0 0] [0 1] [0 1] [1 0] [1 0] [1 1] [1 1]
%e A323863   [0 1] [1 0] [0 0] [1 1] [0 0] [1 1] [0 1] [1 0]
%e A323863 Note that the following are not aperiodic even though their row and column sequences are (independently) aperiodic:
%e A323863   [1 0] [0 1]
%e A323863   [0 1] [1 0]
%t A323863 apermatQ[m_]:=UnsameQ@@Join@@Table[RotateLeft[m,{i,j}],{i,Length[m]},{j,Length[First[m]]}];
%t A323863 Table[Length[Select[(Partition[#,n]&)/@Tuples[{0,1},n^2],apermatQ]],{n,4}]
%Y A323863 Cf. A000031, A000740, A027375, A179043, A265627, A323351.
%Y A323863 Cf. A323860, A323862, A323864, A323865, A323867, A323869.
%K A323863 nonn
%O A323863 0,2
%A A323863 _Gus Wiseman_, Feb 04 2019
%E A323863 a(5) from _Robert Israel_, Feb 04 2019
%E A323863 a(6)-a(7) from _Giovanni Resta_, Feb 05 2019
%E A323863 Terms a(8) and beyond from _Andrew Howroyd_, Aug 21 2019