login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317245 Number of supernormal integer partitions of n. 10
1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 1, 3, 3, 4, 2, 4, 5, 6, 6, 10, 7, 10, 9, 9, 10, 11, 12, 12, 21, 12, 18, 17, 21, 19, 28, 23, 28, 26, 27, 24, 32, 29, 36, 34, 46, 42, 55, 48, 65, 65, 74, 70, 88, 81, 83, 103, 112, 129, 153, 157, 190, 205, 210, 242, 283, 276, 321 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

An integer partition is supernormal if either (1) it is of the form 1^n for some n >= 0, or (2a) it spans an initial interval of positive integers, and (2b) its multiplicities, sorted in weakly decreasing order, are themselves a supernormal integer partition.

LINKS

Table of n, a(n) for n=0..68.

EXAMPLE

The a(10) = 4 supernormal integer partitions are (4321), (33211), (322111), (1111111111).

The a(21) = 10 supernormal integer partitions:

  (654321),

  (4443321),

  (44432211), (44333211), (44332221),

  (4432221111), (4333221111), (4332222111),

  (433322211),

  (111111111111111111111).

MATHEMATICA

supnrm[q_]:=Or[q=={}||Union[q]=={1}, And[Union[q]==Range[Max[q]], supnrm[Sort[Length/@Split[q], Greater]]]];

Table[Length[Select[IntegerPartitions[n], supnrm]], {n, 0, 30}]

CROSSREFS

Cf. A000041, A181819, A182850, A182857, A275870, A304660, A305563, A317081, A317086, A317088, A317246.

Sequence in context: A086394 A029226 A093354 * A109701 A124751 A103374

Adjacent sequences:  A317242 A317243 A317244 * A317246 A317247 A317248

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 24 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 25 16:04 EDT 2019. Contains 322461 sequences. (Running on oeis4.)