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A317245 Number of supernormal integer partitions of n. 27
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 * A332277 A109701 A124751

Adjacent sequences:  A317242 A317243 A317244 * A317246 A317247 A317248

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 24 2018

STATUS

approved

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Last modified May 14 03:00 EDT 2021. Contains 343872 sequences. (Running on oeis4.)