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A329137 Number of integer partitions of n whose differences are an aperiodic word. 3
1, 1, 2, 2, 4, 6, 8, 14, 20, 25, 39, 54, 69, 99, 130, 167, 224, 292, 373, 483, 620, 773, 993, 1246, 1554, 1946, 2421, 2987, 3700, 4548, 5575, 6821, 8330, 10101, 12287, 14852, 17935, 21599, 25986, 31132, 37295, 44539, 53112, 63212, 75123, 89055, 105503, 124682 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A sequence is aperiodic if its cyclic rotations are all different.
LINKS
FORMULA
a(n) + A329144(n) = A000041(n).
EXAMPLE
The a(1) = 1 through a(7) = 14 partitions:
(1) (2) (3) (4) (5) (6) (7)
(1,1) (2,1) (2,2) (3,2) (3,3) (4,3)
(3,1) (4,1) (4,2) (5,2)
(2,1,1) (2,2,1) (5,1) (6,1)
(3,1,1) (4,1,1) (3,2,2)
(2,1,1,1) (2,2,1,1) (3,3,1)
(3,1,1,1) (4,2,1)
(2,1,1,1,1) (5,1,1)
(2,2,2,1)
(3,2,1,1)
(4,1,1,1)
(2,2,1,1,1)
(3,1,1,1,1)
(2,1,1,1,1,1)
With differences:
() () () () () () ()
(0) (1) (0) (1) (0) (1)
(2) (3) (2) (3)
(1,0) (0,1) (4) (5)
(2,0) (3,0) (0,2)
(1,0,0) (0,1,0) (1,0)
(2,0,0) (2,1)
(1,0,0,0) (4,0)
(0,0,1)
(1,1,0)
(3,0,0)
(0,1,0,0)
(2,0,0,0)
(1,0,0,0,0)
MATHEMATICA
aperQ[q_]:=Array[RotateRight[q, #1]&, Length[q], 1, UnsameQ];
Table[Length[Select[IntegerPartitions[n], aperQ[Differences[#]]&]], {n, 0, 30}]
CROSSREFS
The Heinz numbers of these partitions are given by A329135.
The periodic version is A329144.
The augmented version is A329136.
Aperiodic binary words are A027375.
Aperiodic compositions are A000740.
Numbers whose binary expansion is aperiodic are A328594.
Numbers whose prime signature is aperiodic are A329139.
Sequence in context: A291055 A266949 A255710 * A239851 A153958 A216214
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 09 2019
STATUS
approved

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Last modified April 16 08:27 EDT 2024. Contains 371698 sequences. (Running on oeis4.)