A375297 Number of integer compositions of n matching both of the dashed patterns 23-1 and 1-32.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 21, 68, 199, 545, 1410, 3530, 8557, 20255, 46968, 107135, 240927, 535379, 1177435, 2566618, 5551456

Offset

0,11

Comments

Also the number of integer compositions of n whose leaders of maximal weakly increasing runs are not weakly decreasing and whose reverse satisfies the same condition.

Links

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

Wikipedia, Permutation pattern.

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

Example

The a(0) = 0 through a(11) = 21 compositions:
  .  .  .  .  .  .  .  .  .  (12321)  (1342)    (1352)
                                      (2431)    (2531)
                                      (12421)   (11342)
                                      (13231)   (12431)
                                      (112321)  (12521)
                                      (123211)  (13241)
                                                (13421)
                                                (14231)
                                                (23132)
                                                (24311)
                                                (112421)
                                                (113231)
                                                (122321)
                                                (123212)
                                                (123221)
                                                (124211)
                                                (132311)
                                                (212321)
                                                (1112321)
                                                (1123211)
                                                (1232111)

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], MatchQ[#, {___, y_, z_, ___, x_, ___}/; x<y<z]&&MatchQ[#, {___, x_, ___, z_, y_, ___}/; x<y<z]&]], {n, 0, 15}]

Crossrefs

For leaders of identical runs we have A332834.

For just one of the two conditions we have A374636, ranks A375137/A375138.

These compositions are ranked by A375407.

A003242 counts anti-runs, ranks A333489.

A011782 counts compositions.

A106356 counts compositions by number of maximal anti-runs.

A238130, A238279, A333755 count compositions by number of runs.

A274174 counts contiguous compositions, ranks A374249.

A335456 counts patterns matched by compositions.

Cf. A000041, A056823, A188920, A189076, A238343, A333213, A335514, A374631, A374632, A374635, A374681.

Sequence in context: A306089 A107653 A123653 * A364636 A318943 A200761

Adjacent sequences: A375294 A375295 A375296 * A375298 A375299 A375300

Keyword

nonn,more

Author

Gus Wiseman, Aug 23 2024

Status

approved