A353403 Number of compositions of n whose own reversed run-lengths are a subsequence (not necessarily consecutive).

1, 1, 0, 0, 3, 2, 5, 12, 16, 30, 45, 94, 159, 285, 477, 864, 1487, 2643

Offset: 0

Author

Gus Wiseman, May 15 2022

Keywords

• nonn
• more

Examples

			The a(0) = 1 through a(7) = 12 compositions:
  ()  (1)  .  .  (22)   (1121)  (1113)  (1123)
                 (112)  (1211)  (1122)  (1132)
                 (211)          (1221)  (2311)
                                (2211)  (3211)
                                (3111)  (11131)
                                        (11212)
                                        (11221)
                                        (12112)
                                        (12211)
                                        (13111)
                                        (21121)
                                        (21211)
		

Crossrefs

The non-reversed version is A353390, ranked by A353402, partitions A325702.

The non-reversed recursive version is A353391, ranked by A353431.

The non-reversed consecutive case is A353392, ranked by A353432.

The non-reversed recursive consecutive version is A353430.

A003242 counts anti-run compositions, ranked by A333489.

A011782 counts compositions.

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.

Cf. A005811, A032020, A103295, A114640, A165413, A324572, A333755, A353400, A353401, A353426.

Programs

Mathematica

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