A353390 Number of compositions of n whose own run-lengths are a subsequence (not necessarily consecutive).

1, 1, 0, 0, 1, 2, 3, 2, 2, 8, 17, 26, 43, 77, 129, 210, 351, 569

Offset

0,6

Links

Table of n, a(n) for n=0..17.

Example

The a(0) = 1 through a(9) = 8 compositions (empty columns indicated by dots):
  ()  (1)  .  .  (22)  (122)  (1122)  (11221)  (21122)  (333)
                       (221)  (1221)  (12211)  (22112)  (22113)
                              (2211)                    (22122)
                                                        (31122)
                                                        (121122)
                                                        (122112)
                                                        (211221)
                                                        (221121)
For example, the composition y = (2,2,3,3,1) has run-lengths (2,2,1), which form a (non-consecutive) subsequence, so y is counted under a(11).

Mathematica

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

Crossrefs

The version for partitions is A325702.

The recursive version is A353391, ranked by A353431.

The consecutive case is A353392, ranked by A353432.

These compositions are ranked by A353402.

The reverse version is A353403.

The recursive consecutive version is A353430.

A003242 counts anti-run compositions, ranked by A333489.

A011782 counts compositions.

A047966 counts uniform partitions, compositions A329738.

A169942 counts Golomb rulers, ranked by A333222.

A325676 counts knapsack compositions, ranked by A333223, partitions A108917.

A325705 counts partitions containing all of their distinct multiplicities.

A329739 counts compositions with all distinct run-lengths, for runs A351013.

A353400 counts compositions with all run-lengths > 2.

Cf. A005811, A103295, A114901, A181591, A238279, A242882, A324572, A333755, A351017, A353401, A353426.

Sequence in context: A365407 A366782 A134142 * A298310 A138680 A171684

Adjacent sequences: A353387 A353388 A353389 * A353391 A353392 A353393

Keyword

nonn,more

Author

Gus Wiseman, May 15 2022

Status

approved