A319811 Number of totally aperiodic integer partitions of n.

1, 1, 2, 3, 6, 7, 14, 17, 27, 34, 55, 63, 99, 117, 162, 203, 286, 333, 469, 558, 737, 903, 1196, 1414, 1860, 2232, 2839, 3422, 4359, 5144, 6531, 7762, 9617, 11479, 14182, 16715, 20630, 24333, 29569, 34890, 42335, 49515, 59871, 70042, 83810, 98105, 117152

Offset

1,3

Comments

An integer partition is totally aperiodic iff either it is strict or it is aperiodic with totally aperiodic multiplicities.

Links

Table of n, a(n) for n=1..47.

Example

The a(6) = 7 aperiodic integer partitions are: (6), (51), (42), (411), (321), (3111), (21111). The first aperiodic integer partition that is not totally aperiodic is (432211).

Mathematica

totaperQ[m_]:=Or[UnsameQ@@m, And[GCD@@Length/@Split[Sort[m]]==1, totaperQ[Sort[Length/@Split[Sort[m]]]]]];
Table[Length[Select[IntegerPartitions[n], totaperQ]], {n, 30}]

Crossrefs

Cf. A000837, A018783, A047966, A098859, A100953, A305563, A319149, A319160, A319162, A319163, A319164, A319810.

Sequence in context: A018606 A117087 A322367 * A000837 A200144 A056498

Adjacent sequences: A319808 A319809 A319810 * A319812 A319813 A319814

Keyword

nonn

Author

Gus Wiseman, Sep 28 2018

Status

approved