OFFSET
1,3
COMMENTS
An integer partition is uniformly normal if either (1) it is of the form (x, x, ..., x) for some x > 0, or (2a) it spans an initial interval of positive integers, and (2b) its multiplicities, sorted in weakly decreasing order, are themselves a uniformly normal integer partition.
LINKS
A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp.1-12.
EXAMPLE
The a(6) = 6 uniformly normal integer partitions are (6), (33), (321), (222), (2211), (111111). Missing from this list are (51), (42), (411), (3111), (21111).
The a(21) = 14 uniformly normal integer partitions (n = 21):
(n),
(777),
(654321),
(4443321), (3333333),
(44432211), (44333211), (44332221),
(4432221111), (4333221111), (4332222111),
(433322211),
(22222221111111),
(111111111111111111111).
MATHEMATICA
uninrmQ[q_]:=Or[q=={}||Length[Union[q]]==1, And[Union[q]==Range[Max[q]], uninrmQ[Sort[Length/@Split[q], Greater]]]];
Table[Length[Select[IntegerPartitions[n], uninrmQ]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 01 2018
STATUS
approved