OFFSET
0,4
COMMENTS
Every sequence can be uniquely split into a sequence of non-overlapping runs. For example, the runs of (2,2,1,1,1,3,2,2) are ((2,2),(1,1,1),(3),(2,2)), with sums (4,3,3,4).
EXAMPLE
The a(0) = 0 through a(6) = 16 compositions:
() (1) (2) (3) (4) (5) (6)
(12) (13) (14) (15)
(21) (22) (23) (24)
(31) (32) (33)
(121) (41) (42)
(122) (51)
(131) (123)
(212) (132)
(221) (141)
(213)
(222)
(231)
(312)
(321)
(1212)
(2121)
MATHEMATICA
Table[Length[Union[Total/@Split[#]&/@ Join@@Permutations/@IntegerPartitions[n]]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 20 2022
STATUS
approved