OFFSET
0,5
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:
. . (11) (111) (112) (113) (114)
(211) (311) (411)
(1111) (1112) (1113)
(1121) (1122)
(1211) (1131)
(2111) (1221)
(11111) (1311)
(2112)
(2211)
(3111)
(11112)
(11121)
(11211)
(12111)
(21111)
(111111)
MATHEMATICA
Table[Length[Complement[Join@@Permutations/@IntegerPartitions[n], Total/@Split[#]&/@Join@@Permutations/@IntegerPartitions[n]]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 19 2022
STATUS
approved