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A329144
Number of integer partitions of n whose differences are a periodic word.
4
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, 21, 19, 42, 23, 31, 42, 38, 29, 53, 43, 44, 62, 49, 52, 79, 55, 72, 75, 87, 63, 117, 79, 104, 107, 120, 99, 156, 117, 143, 147
OFFSET
1,6
COMMENTS
A finite sequence is periodic if its cyclic rotations are not all different.
EXAMPLE
The a(n) partitions for n = 3, 6, 8, 9, 12, 15, 16:
111 222 2222 333 444 555 4444
321 11111111 432 543 654 7531
111111 531 642 753 44332
32211 741 852 3332221
111111111 3333 951 4332211
222222 33333 22222222
3222111 54321 1111111111111111
111111111111 322221111
111111111111111
MATHEMATICA
aperQ[q_]:=Array[RotateRight[q, #1]&, Length[q], 1, UnsameQ];
Table[Length[Select[IntegerPartitions[n], !aperQ[Differences[#]]&]], {n, 30}]
CROSSREFS
The Heinz numbers of these partitions are given by A329134.
The augmented version is A329143.
Periodic binary words are A152061.
Periodic compositions are A178472.
Numbers whose binary expansion is periodic are A121016.
Numbers whose prime signature is periodic are A329140.
Sequence in context: A227042 A033765 A033777 * A272071 A033801 A332319
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 10 2019
STATUS
approved