OFFSET
0,2
COMMENTS
By "distinct" we mean equal subsequences are counted only once. For example, the pair (1,1)(1) is counted only once even though (1) is a subsequence of (1,1) in two ways. The version with multiplicity is A025192.
EXAMPLE
The a(3) = 14 pairings of a composition with a chosen subsequence:
(3)() (3)(3)
(21)() (21)(1) (21)(2) (21)(21)
(12)() (12)(1) (12)(2) (12)(12)
(111)() (111)(1) (111)(11) (111)(111)
MATHEMATICA
Table[Sum[Length[Union[Subsets[y]]], {y, Join@@Permutations/@IntegerPartitions[n]}], {n, 0, 6}]
CROSSREFS
The strict case is A032005.
The case of strict subsequences is A236002.
A075900 counts compositions of each part of a partition.
A304961 counts compositions of each part of a strict partition.
A307068 counts strict compositions of each part of a composition.
A336127 counts compositions of each part of a strict composition.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 04 2022
STATUS
approved