A374518 - OEIS

A374518

Number of integer compositions of n whose leaders of anti-runs are distinct.

1, 1, 1, 3, 5, 9, 17, 32, 58, 112, 201, 371, 694, 1276, 2342, 4330, 7958, 14613, 26866, 49303, 90369, 165646, 303342, 555056, 1015069, 1855230

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OFFSET

0,4

COMMENTS

The leaders of 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

Table of n, a(n) for n=0..25.

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

EXAMPLE

The a(0) = 1 through a(6) = 17 compositions:

() (1) (2) (3) (4) (5) (6)

(12) (13) (14) (15)

(21) (31) (23) (24)

(121) (32) (42)

(211) (41) (51)

(122) (123)

(131) (132)

(212) (141)

(311) (213)

(231)

(312)

(321)

(411)

(1212)

(1221)

(2112)

(2121)

MATHEMATICA

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

CROSSREFS

These compositions have ranks A374638.

The complement is counted by A374678.

For partitions instead of compositions we have A375133.

Other types of runs (instead of anti-):

- For leaders of identical runs we have A274174, ranks A374249.

- For leaders of weakly increasing runs we have A374632, ranks A374768.

- For leaders of strictly increasing runs we have A374687, ranks A374698.

- For leaders of weakly decreasing runs we have A374743, ranks A374701.

- For leaders of strictly decreasing runs we have A374761, ranks A374767.

Other types of run-leaders (instead of distinct):

- For identical leaders we have A374517.

- For weakly increasing leaders we have A374681.

- For strictly increasing leaders we have A374679.

- For weakly decreasing leaders we have A374682.

- For strictly decreasing leaders we have A374680.

A003242 counts anti-runs, ranks A333489.

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.

Cf. A188920, A233564, A238343, A333213, A333381, A373949, A374515.

Sequence in context: A000213 A074858 A074860 * A297300 A364543 A213005

Adjacent sequences: A374515 A374516 A374517 * A374519 A374520 A374521

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 01 2024

STATUS

approved