|
|
A355387
|
|
Number of ways to choose a distinct subsequence of an integer composition of n.
|
|
1
|
|
|
1, 2, 5, 14, 37, 98, 259, 682, 1791, 4697, 12303, 32196, 84199, 220087, 575067, 1502176
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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.
|
|
LINKS
|
|
|
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 case of strict subsequences is A236002.
The composable case is A355384, homogeneous without containment A355388.
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.
Cf. A022811, A032020, A063834, A133494, A181591, A323583, A336128, A336130, A336139, A355382, A355383.
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|