OFFSET
0,3
COMMENTS
The weakly decreasing run-leaders of a sequence are obtained by splitting it into maximal weakly decreasing subsequences and taking the first term of each.
LINKS
EXAMPLE
The a(0) = 1 through a(7) = 18 compositions:
() (1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (311) (222) (322)
(2111) (312) (331)
(11111) (321) (412)
(411) (421)
(2211) (511)
(3111) (2221)
(21111) (3112)
(111111) (3121)
(3211)
(4111)
(22111)
(31111)
(211111)
(1111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], Greater@@First/@Split[#, GreaterEqual]&]], {n, 0, 15}]
CROSSREFS
Types of runs (instead of weakly decreasing):
- For leaders of identical runs we have A000041.
- For leaders of weakly increasing runs we have A188920.
- For leaders of anti-runs we have A374680.
- For leaders of strictly increasing runs we have A374689.
- For leaders of strictly decreasing runs we have A374763.
Types of run-leaders (instead of strictly decreasing):
- For weakly increasing leaders we appear to have A188900.
- For identical leaders we have A374742.
- For strictly increasing leaders we have opposite A374634.
- For weakly decreasing leaders we have A374747.
A011782 counts compositions.
A335456 counts patterns matched by compositions.
A374748 counts compositions by sum of leaders of weakly decreasing runs.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2024
EXTENSIONS
a(24)-a(39) from Alois P. Heinz, Jul 26 2024
STATUS
approved