OFFSET
0,6
EXAMPLE
The a(0) = 1 through a(9) = 8 compositions (empty columns indicated by dots):
() (1) . . (22) (122) (1122) (11221) (21122) (333)
(221) (1221) (12211) (22112) (22113)
(2211) (22122)
(31122)
(121122)
(122112)
(211221)
(221121)
For example, the composition y = (2,2,3,3,1) has run-lengths (2,2,1), which form a (non-consecutive) subsequence, so y is counted under a(11).
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], MemberQ[Subsets[#], Length/@Split[#]]&]], {n, 0, 15}]
CROSSREFS
The version for partitions is A325702.
These compositions are ranked by A353402.
The reverse version is A353403.
The recursive consecutive version is A353430.
A011782 counts compositions.
A325705 counts partitions containing all of their distinct multiplicities.
A353400 counts compositions with all run-lengths > 2.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 15 2022
STATUS
approved