OFFSET
0,4
COMMENTS
The leaders of strictly increasing runs in a sequence are obtained by splitting it into maximal strictly increasing subsequences and taking the first term of each.
LINKS
EXAMPLE
The a(0) = 1 through a(7) = 15 compositions:
() (1) (2) (3) (4) (5) (6) (7)
(12) (13) (14) (15) (16)
(21) (31) (23) (24) (25)
(32) (42) (34)
(41) (51) (43)
(122) (123) (52)
(212) (132) (61)
(213) (124)
(231) (133)
(312) (142)
(321) (214)
(241)
(313)
(412)
(421)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], UnsameQ@@First/@Split[#, Less]&]], {n, 0, 15}]
CROSSREFS
Ranked by A374698.
Types of runs (instead of strictly increasing):
Types of run-leaders (instead of distinct):
- For strictly increasing leaders we have A374688.
- For strictly decreasing leaders we have A374689.
- For weakly increasing leaders we have A374690.
- For weakly decreasing leaders we have A374697.
A011782 counts compositions.
A335456 counts patterns matched by compositions.
A374683 lists leaders of strictly increasing runs of standard compositions.
A374700 counts compositions by sum of leaders of strictly increasing runs.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 27 2024
STATUS
approved