cp's OEIS Frontend

A329144 Number of integer partitions of n whose differences are a periodic word.

%I A329144 #7 Nov 10 2019 20:28:51
%S A329144 0,0,1,1,1,3,1,2,5,3,2,8,2,5,9,7,5,12,7,7,19,9,9,21,12,15,23,18,17,29,
%T A329144 21,19,42,23,31,42,38,29,53,43,44,62,49,52,79,55,72,75,87,63,117,79,
%U A329144 104,107,120,99,156,117,143,147
%N A329144 Number of integer partitions of n whose differences are a periodic word.
%C A329144 A finite sequence is periodic if its cyclic rotations are not all different.
%e A329144 The a(n) partitions for n = 3, 6, 8, 9, 12, 15, 16:
%e A329144   111  222     2222      333        444           555              4444
%e A329144        321     11111111  432        543           654              7531
%e A329144        111111            531        642           753              44332
%e A329144                          32211      741           852              3332221
%e A329144                          111111111  3333          951              4332211
%e A329144                                     222222        33333            22222222
%e A329144                                     3222111       54321            1111111111111111
%e A329144                                     111111111111  322221111
%e A329144                                                   111111111111111
%t A329144 aperQ[q_]:=Array[RotateRight[q,#1]&,Length[q],1,UnsameQ];
%t A329144 Table[Length[Select[IntegerPartitions[n],!aperQ[Differences[#]]&]],{n,30}]
%Y A329144 The Heinz numbers of these partitions are given by A329134.
%Y A329144 The augmented version is A329143.
%Y A329144 Periodic binary words are A152061.
%Y A329144 Periodic compositions are A178472.
%Y A329144 Numbers whose binary expansion is periodic are A121016.
%Y A329144 Numbers whose prime signature is periodic are A329140.
%Y A329144 Cf. A000740, A027375, A059966, A328594, A328596, A329132, A329135, A329136.
%K A329144 nonn
%O A329144 1,6
%A A329144 _Gus Wiseman_, Nov 10 2019