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.

1, 1, 1, 1, 2, 1, 3, 1, 1, 4, 5, 7, 9, 11, 15, 16, 22, 25, 37, 37, 45

Offset: 0

Author

Gus Wiseman, May 16 2022

Keywords

• nonn
• more

Examples

			The a(n) compositions for selected n (A..E = 10..14):
  n=4:  n=6:    n=9:      n=10:     n=12:     n=14:
-----------------------------------------------------------
  (4)   (6)     (9)       (A)       (C)       (E)
  (22)  (1122)  (333)     (2233)    (2244)    (2255)
        (2211)  (121122)  (3322)    (4422)    (5522)
                (221121)  (131122)  (151122)  (171122)
                          (221131)  (221124)  (221126)
                                    (221142)  (221135)
                                    (221151)  (221153)
                                    (241122)  (221162)
                                    (421122)  (221171)
                                              (261122)
                                              (351122)
                                              (531122)
                                              (621122)
                                              (122121122)
                                              (221121221)
		

Crossrefs

Non-recursive non-consecutive version: counted by A353390, ranked by A353402, reverse A353403, partitions A325702.

Non-consecutive version: A353391, ranked by A353431, partitions A353426.

Non-recursive version: A353392, ranked by A353432.

A003242 counts anti-run compositions, ranked by A333489.

A011782 counts compositions.

A114901 counts compositions with no runs of length 1.

A169942 counts Golomb rulers, ranked by A333222.

A325676 counts knapsack compositions, ranked by A333223.

A329738 counts uniform compositions, partitions A047966.

A329739 counts compositions with all distinct run-lengths.

Cf. A005811, A032020, A103295, A114640, A165413, A242882, A325705, A333755, A351013, A353400, A353401.

Programs

Mathematica

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]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],yoyQ]],{n,0,15}]