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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
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
Sequence in context: A086394 A029226 A093354 * A332277 A109701 A124751
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 24 2018
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)