cp's OEIS Frontend

A353391 Number of compositions of n that are empty, a singleton, or whose run-lengths are a subsequence that is already counted.

%I A353391 #6 May 16 2022 17:23:46
%S A353391 1,1,1,1,2,1,3,1,1,4,5,7,9,11,15,22,38,45,87,93
%N A353391 Number of compositions of n that are empty, a singleton, or whose run-lengths are a subsequence that is already counted.
%e A353391 The a(9) = 4 through a(14) = 15 compositions (A..E = 10..14):
%e A353391   (9)       (A)       (B)       (C)       (D)       (E)
%e A353391   (333)     (2233)    (141122)  (2244)    (161122)  (2255)
%e A353391   (121122)  (3322)    (221123)  (4422)    (221125)  (5522)
%e A353391   (221121)  (131122)  (221132)  (151122)  (221134)  (171122)
%e A353391             (221131)  (221141)  (221124)  (221143)  (221126)
%e A353391                       (231122)  (221142)  (221152)  (221135)
%e A353391                       (321122)  (221151)  (221161)  (221153)
%e A353391                                 (241122)  (251122)  (221162)
%e A353391                                 (421122)  (341122)  (221171)
%e A353391                                           (431122)  (261122)
%e A353391                                           (521122)  (351122)
%e A353391                                                     (531122)
%e A353391                                                     (621122)
%e A353391                                                     (122121122)
%e A353391                                                     (221121221)
%t A353391 yosQ[y_]:=Length[y]<=1||MemberQ[Subsets[y],Length/@Split[y]]&&yosQ[Length/@Split[y]];
%t A353391 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],yosQ]],{n,0,15}]
%Y A353391 The non-recursive version is A353390, ranked by A353402.
%Y A353391 The non-recursive consecutive version is A353392, ranked by A353432.
%Y A353391 The non-recursive reverse version is A353403.
%Y A353391 The unordered version is A353426, ranked by A353393 (nonprime A353389).
%Y A353391 The consecutive version is A353430.
%Y A353391 These compositions are ranked by A353431.
%Y A353391 A003242 counts anti-run compositions, ranked by A333489.
%Y A353391 A011782 counts compositions.
%Y A353391 A329738 counts uniform compositions, partitions A047966.
%Y A353391 A114901 counts compositions with no runs of length 1.
%Y A353391 A169942 counts Golomb rulers, ranked by A333222.
%Y A353391 A325676 counts knapsack compositions, ranked by A333223.
%Y A353391 A325705 counts partitions containing all of their distinct multiplicities.
%Y A353391 A329739 counts compositions with all distinct run-length.
%Y A353391 Cf. A005811, A032020, A103295, A114640, A165413, A181591, A242882, A324572, A325702, A333755, A351013, A353401.
%K A353391 nonn,more
%O A353391 0,5
%A A353391 _Gus Wiseman_, May 15 2022