A319153 Number of integer partitions of n that reduce to 2, meaning their Heinz number maps to 2 under A304464.

0, 2, 1, 3, 5, 7, 12, 17, 24, 33, 44, 57, 76, 100, 129, 168, 214, 282, 355, 462, 586, 755, 937, 1202, 1493, 1900, 2349, 2944, 3621, 4520, 5514, 6813, 8298, 10150, 12240, 14918, 17931, 21654, 25917, 31081, 37029, 44256, 52474, 62405, 73724, 87378, 102887

Offset

1,2

Comments

Start with an integer partition y of n. Given a multiset, take the multiset of its multiplicities. Repeat until a multiset of size 1 is obtained. If this multiset is {2}, we say that y reduces to 2. For example, we have (3211) -> (211) -> (21) -> (11) -> (2), so (3211) reduces to 2.

Links

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

Example

The a(7) = 12 partitions:
  (43), (52), (61),
  (322), (331), (511),
  (2221), (3211), (4111),
  (22111), (31111),
  (211111).

Mathematica

Table[Length[Select[IntegerPartitions[n], NestWhile[Sort[Length/@Split[#]]&, #, Length[#]>1&]=={2}&]], {n, 30}]

Crossrefs

Cf. A000837, A098859, A181819, A182850, A304464, A304465, A304634, A305563, A317245, A319149.

Sequence in context: A006769 A075643 A076074 * A286390 A135017 A070168

Adjacent sequences: A319150 A319151 A319152 * A319154 A319155 A319156

Keyword

nonn

Author

Gus Wiseman, Sep 12 2018

Status

approved