OFFSET
0,4
COMMENTS
The leaders of strictly decreasing runs in a sequence are obtained by splitting it into maximal strictly decreasing subsequences and taking the first term of each.
LINKS
EXAMPLE
The composition (3,1,4,3,2,1,2,8) has strictly decreasing runs ((3,1),(4,3,2,1),(2),(8)), with leaders (3,4,2,1), so is counted under a(24).
The a(0) = 1 through a(6) = 13 compositions:
() (1) (2) (3) (4) (5) (6)
(12) (13) (14) (15)
(21) (31) (23) (24)
(121) (32) (42)
(211) (41) (51)
(131) (123)
(311) (132)
(141)
(213)
(231)
(312)
(321)
(411)
MATHEMATICA
Table[Length[Select[Join @@ Permutations/@IntegerPartitions[n], UnsameQ@@First/@Split[#, Greater]&]], {n, 0, 15}]
CROSSREFS
Ranked by A374767.
For partitions instead of compositions we have A375133.
Other types of runs:
Other types of run-leaders:
- For strictly increasing leaders we have A374762.
- For strictly decreasing leaders we have A374763.
- For weakly increasing leaders we have A374764.
- For weakly decreasing leaders we have A374765.
A011782 counts compositions.
A374700 counts compositions by sum of leaders of strictly increasing runs.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 29 2024
STATUS
approved