OFFSET
0,7
COMMENTS
The leaders of maximal 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) = 0 through a(8) = 14 compositions:
. . . . . (122) (1122) (133) (233)
(1221) (1222) (1133)
(11122) (1223)
(11221) (1322)
(12211) (1331)
(11222)
(12122)
(12212)
(12221)
(21122)
(111122)
(111221)
(112211)
(122111)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], !GreaterEqual@@First/@Split[#, UnsameQ]&]], {n, 0, 15}]
CROSSREFS
The complement is counted by A374682.
Other types of runs (instead of anti-):
- For leaders of identical runs we have A056823.
Other types of run-leaders (instead of weakly decreasing):
- For weakly increasing leaders we have complement A374681.
- For strictly increasing leaders we have complement complement A374679.
- For strictly decreasing leaders we have complement 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.
A333381 counts maximal anti-runs in standard compositions.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 06 2024
STATUS
approved