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.
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 24 2018
STATUS
approved