cp's OEIS Frontend

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

%I A353390 #6 May 16 2022 10:02:31
%S A353390 1,1,0,0,1,2,3,2,2,8,17,26,43,77,129,210,351,569
%N A353390 Number of compositions of n whose own run-lengths are a subsequence (not necessarily consecutive).
%e A353390 The a(0) = 1 through a(9) = 8 compositions (empty columns indicated by dots):
%e A353390   ()  (1)  .  .  (22)  (122)  (1122)  (11221)  (21122)  (333)
%e A353390                        (221)  (1221)  (12211)  (22112)  (22113)
%e A353390                               (2211)                    (22122)
%e A353390                                                         (31122)
%e A353390                                                         (121122)
%e A353390                                                         (122112)
%e A353390                                                         (211221)
%e A353390                                                         (221121)
%e A353390 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).
%t A353390 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], MemberQ[Subsets[#],Length/@Split[#]]&]],{n,0,15}]
%Y A353390 The version for partitions is A325702.
%Y A353390 The recursive version is A353391, ranked by A353431.
%Y A353390 The consecutive case is A353392, ranked by A353432.
%Y A353390 These compositions are ranked by A353402.
%Y A353390 The reverse version is A353403.
%Y A353390 The recursive consecutive version is A353430.
%Y A353390 A003242 counts anti-run compositions, ranked by A333489.
%Y A353390 A011782 counts compositions.
%Y A353390 A047966 counts uniform partitions, compositions A329738.
%Y A353390 A169942 counts Golomb rulers, ranked by A333222.
%Y A353390 A325676 counts knapsack compositions, ranked by A333223, partitions A108917.
%Y A353390 A325705 counts partitions containing all of their distinct multiplicities.
%Y A353390 A329739 counts compositions with all distinct run-lengths, for runs A351013.
%Y A353390 A353400 counts compositions with all run-lengths > 2.
%Y A353390 Cf. A005811, A103295, A114901, A181591, A238279, A242882, A324572, A333755, A351017, A353401, A353426.
%K A353390 nonn,more
%O A353390 0,6
%A A353390 _Gus Wiseman_, May 15 2022