login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319153 Number of integer partitions of n that reduce to 2, meaning their Heinz number maps to 2 under A304464. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 16 17:01 EDT 2021. Contains 343050 sequences. (Running on oeis4.)