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

Author

Gus Wiseman, May 15 2022

Keywords

• nonn
• more

Examples

			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).
		

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.

Programs

Mathematica

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