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 A323867 Number of aperiodic arrays of positive integers summing to n. 12
 1, 1, 1, 5, 11, 33, 57, 157, 303, 683, 1358, 2974, 5932, 12560, 25328, 52400, 106256, 217875, 441278, 899955, 1822703, 3701401, 7491173, 15178253, 30691135, 62085846, 125435689, 253414326, 511547323, 1032427635, 2082551931, 4199956099, 8466869525, 17064777665 (list; graph; refs; listen; history; text; internal format)
 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 (GAP) List([0..30], A323867); # See A323861 for code; Andrew Howroyd, Aug 21 2019 CROSSREFS Cf. A000670, A000740, A027375, A101509. Cf. A323860, A323861, A323862, A323863, A323864, A323866, A323869. Sequence in context: A106908 A107442 A349611 * A280540 A077917 A127864 Adjacent sequences:  A323864 A323865 A323866 * A323868 A323869 A323870 KEYWORD nonn AUTHOR Gus Wiseman, Feb 04 2019 EXTENSIONS Terms a(16) and beyond from Andrew Howroyd, Aug 21 2019 STATUS approved

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)