cp's OEIS Frontend

A353430 Number of integer compositions of n that are empty, a singleton, or whose own run-lengths are a consecutive subsequence that is already counted.

%I A353430 #6 May 17 2022 07:24:58
%S A353430 1,1,1,1,2,1,3,1,1,4,5,7,9,11,15,16,22,25,37,37,45
%N A353430 Number of integer compositions of n that are empty, a singleton, or whose own run-lengths are a consecutive subsequence that is already counted.
%e A353430 The a(n) compositions for selected n (A..E = 10..14):
%e A353430   n=4:  n=6:    n=9:      n=10:     n=12:     n=14:
%e A353430 -----------------------------------------------------------
%e A353430   (4)   (6)     (9)       (A)       (C)       (E)
%e A353430   (22)  (1122)  (333)     (2233)    (2244)    (2255)
%e A353430         (2211)  (121122)  (3322)    (4422)    (5522)
%e A353430                 (221121)  (131122)  (151122)  (171122)
%e A353430                           (221131)  (221124)  (221126)
%e A353430                                     (221142)  (221135)
%e A353430                                     (221151)  (221153)
%e A353430                                     (241122)  (221162)
%e A353430                                     (421122)  (221171)
%e A353430                                               (261122)
%e A353430                                               (351122)
%e A353430                                               (531122)
%e A353430                                               (621122)
%e A353430                                               (122121122)
%e A353430                                               (221121221)
%t A353430 yoyQ[y_]:=Length[y]<=1||MemberQ[Join@@Table[Take[y,{i,j}],{i,Length[y]},{j,i,Length[y]}],Length/@Split[y]]&&yoyQ[Length/@Split[y]];
%t A353430 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],yoyQ]],{n,0,15}]
%Y A353430 Non-recursive non-consecutive version: counted by A353390, ranked by A353402, reverse A353403, partitions A325702.
%Y A353430 Non-consecutive version: A353391, ranked by A353431, partitions A353426.
%Y A353430 Non-recursive version: A353392, ranked by A353432.
%Y A353430 A003242 counts anti-run compositions, ranked by A333489.
%Y A353430 A011782 counts compositions.
%Y A353430 A114901 counts compositions with no runs of length 1.
%Y A353430 A169942 counts Golomb rulers, ranked by A333222.
%Y A353430 A325676 counts knapsack compositions, ranked by A333223.
%Y A353430 A329738 counts uniform compositions, partitions A047966.
%Y A353430 A329739 counts compositions with all distinct run-lengths.
%Y A353430 Cf. A005811, A032020, A103295, A114640, A165413, A242882, A325705, A333755, A351013, A353400, A353401.
%K A353430 nonn,more
%O A353430 0,5
%A A353430 _Gus Wiseman_, May 16 2022