A374640 Number of integer compositions of n whose leaders of maximal anti-runs are not identical.

0, 0, 0, 0, 1, 3, 7, 18, 43, 96, 211, 463, 992, 2112, 4462, 9347, 19495, 40480, 83690, 172478, 354455, 726538, 1486024, 3033644, 6182389, 12580486

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 a(0) = 0 through a(7) = 18 compositions:
  .  .  .  .  (211)  (122)   (411)    (133)
                     (311)   (1122)   (322)
                     (2111)  (1221)   (511)
                             (2112)   (1222)
                             (2211)   (2113)
                             (3111)   (2311)
                             (21111)  (3112)
                                      (3211)
                                      (4111)
                                      (11122)
                                      (11221)
                                      (12211)
                                      (21112)
                                      (21121)
                                      (21211)
                                      (22111)
                                      (31111)
                                      (211111)
		

Links

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

Crossrefs

For partitions instead of compositions we have A239955.

The complement is counted by A374517, ranks A374519.

Compositions of this type are ranked by A374520, complement A374519.

For distinct instead of identical leaders we have A374678, ranks A374639, complement A374518, ranks A374638.

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, A238424, A272919, A333213, A373949, A374515, A374700.

Programs

Mathematica

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