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A374678
Number of integer compositions of n whose leaders of maximal anti-runs are not distinct.
12
0, 0, 1, 1, 3, 7, 15, 32, 70, 144, 311, 653, 1354, 2820, 5850, 12054, 24810, 50923, 104206, 212841, 433919, 882930, 1793810, 3639248, 7373539, 14921986
OFFSET
0,5
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.
EXAMPLE
The anti-runs of y = (1,1,2,2) are ((1),(1,2),(2)) with leaders (1,1,2) so y is counted under a(6).
The a(0) = 0 through a(6) = 15 compositions:
. . (11) (111) (22) (113) (33)
(112) (221) (114)
(1111) (1112) (222)
(1121) (1113)
(1211) (1122)
(2111) (1131)
(11111) (1311)
(2211)
(3111)
(11112)
(11121)
(11211)
(12111)
(21111)
(111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], !UnsameQ@@First/@Split[#, UnsameQ]&]], {n, 0, 15}]
CROSSREFS
For constant runs we have A335548, complement A274174, ranks A374249.
The complement is counted by A374518, ranks A374638.
For weakly increasing runs we have complement A374632, ranks A374768.
Compositions of this type are ranked by A374639.
For identical instead of distinct leaders we have A374640, ranks A374520, complement A374517, ranks A374519.
A003242 counts anti-runs, ranks A333489.
A065120 gives leaders of standard compositions.
A106356 counts compositions by number of maximal anti-runs.
A238279 counts compositions by number of maximal runs
A274174 counts contiguous compositions, ranks A374249.
Sequence in context: A026745 A139333 A099444 * A132402 A137166 A101890
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 06 2024
STATUS
approved