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

Author

Gus Wiseman, Sep 12 2018

Keywords

• nonn

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.

Examples

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

Crossrefs

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

Programs

Mathematica

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