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.

LINKS

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

Compositions of this type are ranked by A374639.

For identical instead of distinct leaders we have A374640, ranks A374520, complement A374517, ranks A374519.

A065120 gives leaders of standard compositions.

A106356 counts compositions by number of maximal anti-runs.

A238279 counts compositions by number of maximal runs

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 06 2024

STATUS

approved