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A323869 Number of aperiodic matrices of size n whose entries cover an initial interval of positive integers.

%I A323869 #9 Aug 23 2019 00:58:17
%S A323869 1,4,24,212,1080,18672,94584,2182752,21261708,408988080,3245265144,
%T A323869 168549358368,1053716696760,42565371692592,921132763909200,
%U A323869 26578273403903040,260741534058271800,20313207979498492344,185603174638656822264,16066126777465282744800,324499299994016295338064
%N A323869 Number of aperiodic matrices of size n whose entries cover an initial interval of positive integers.
%C A323869 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 A323869 Andrew Howroyd, <a href="/A323869/b323869.txt">Table of n, a(n) for n = 1..200</a>
%F A323869 a(n) = n*A323871(n). - _Andrew Howroyd_, Aug 21 2019
%e A323869 The a(3) = 24 matrices:
%e A323869   [123][132][213][312][231][321][122][211][112][221][121][212]
%e A323869 .
%e A323869   [1][1][2][3][2][3][1][2][1][2][1][2]
%e A323869   [2][3][1][1][3][2][2][1][1][2][2][1]
%e A323869   [3][2][3][2][1][1][2][1][2][1][1][2]
%t A323869 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A323869 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]}];
%t A323869 apermatQ[m_]:=UnsameQ@@Join@@Table[RotateLeft[m,{i,j}],{i,Length[m]},{j,Length[First[m]]}];
%t A323869 Table[Length[Select[nrmmats[n],apermatQ]],{n,6}]
%o A323869 (GAP) List([1..30], A323869); # See A323861 for code; _Andrew Howroyd_, Aug 21 2019
%Y A323869 Cf. A000670, A000740, A027375, A060223, A265627.
%Y A323869 Cf. A323860, A323864, A323867, A323868, A323871.
%K A323869 nonn
%O A323869 1,2
%A A323869 _Gus Wiseman_, Feb 04 2019
%E A323869 Terms a(9) and beyond from _Andrew Howroyd_, Aug 21 2019