A374678 Number of integer compositions of n whose leaders of maximal anti-runs are not distinct.

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

Author

Gus Wiseman, Aug 06 2024

Keywords

• nonn
• more

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.

Examples

			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)
		

Links

• Gus Wiseman, Sequences counting and ranking compositions by their leaders (for six types of runs).

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.

Cf. A034296, A188920, A189076, A238343, A239955, A333213, A373949, A374515.

Programs

Mathematica

Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n],!UnsameQ@@First/@Split[#,UnsameQ]&]],{n,0,15}]