OFFSET
0,4
COMMENTS
The leaders of anti-runs in a sequence are obtained by splitting it into maximal consecutive anti-runs (sequences with no adjacent equal terms) and taking the first term of each.
LINKS
EXAMPLE
The a(0) = 1 through a(6) = 16 compositions:
() (1) (2) (3) (4) (5) (6)
(12) (13) (14) (15)
(21) (31) (23) (24)
(121) (32) (42)
(211) (41) (51)
(131) (123)
(212) (132)
(311) (141)
(213)
(231)
(312)
(321)
(411)
(1212)
(2112)
(2121)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], Greater@@First/@Split[#, UnsameQ]&]], {n, 0, 15}]
CROSSREFS
For distinct but not necessarily decreasing leaders we have A374518.
For partitions instead of compositions we have A375133.
Other types of runs (instead of anti-):
- For leaders of identical runs we have A000041.
- For leaders of weakly increasing runs we have A188920.
- For leaders of weakly decreasing runs we have A374746.
- For leaders of strictly decreasing runs we have A374763.
- For leaders of strictly increasing runs we have A374689.
Other types of run-leaders (instead of strictly decreasing):
- For weakly increasing leaders we have A374681.
- For strictly increasing leaders we have A374679.
- For weakly decreasing leaders we have A374682.
A106356 counts compositions by number of maximal anti-runs.
A238279 counts compositions by number of maximal runs
A238424 counts partitions whose first differences are an anti-run.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 01 2024
STATUS
approved