%I #7 May 16 2022 17:24:20

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

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

%e The a(0) = 1 through a(7) = 12 compositions:

%e () (1) . . (22) (1121) (1113) (1123)

%e (112) (1211) (1122) (1132)

%e (211) (1221) (2311)

%e (2211) (3211)

%e (3111) (11131)

%e (11212)

%e (11221)

%e (12112)

%e (12211)

%e (13111)

%e (21121)

%e (21211)

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

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

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

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

%Y The non-reversed recursive consecutive version is A353430.

%Y A003242 counts anti-run compositions, ranked by A333489.

%Y A011782 counts compositions.

%Y A169942 counts Golomb rulers, ranked by A333222.

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

%Y A325705 counts partitions containing all of their distinct multiplicities.

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

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

%K nonn,more

%O 0,5

%A _Gus Wiseman_, May 15 2022