OFFSET
0,3
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(5) = 14 compositions:
() (1) (2) (3) (4) (5)
(11) (12) (13) (14)
(21) (22) (23)
(111) (31) (32)
(112) (41)
(121) (113)
(1111) (122)
(131)
(212)
(221)
(1112)
(1121)
(1211)
(11111)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], LessEqual@@First/@Split[#, UnsameQ]&]], {n, 0, 15}]
CROSSREFS
For partitions instead of compositions we have A034296.
Other types of runs (instead of anti-):
- For leaders of constant runs we have A000041.
- For leaders of weakly decreasing runs we have A188900.
- For leaders of weakly increasing runs we have A374635.
- For leaders of strictly increasing runs we have A374690.
- For leaders of strictly decreasing runs we have A374764.
Other types of run-leaders (instead of weakly increasing):
- For strictly increasing leaders we have A374679.
- For weakly decreasing leaders we have A374682.
- For strictly decreasing leaders we have A374680.
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