A319153 - OEIS

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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

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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