A338169 A list of all finite sequences of distinct positive integers sorted by their maximum value, then lexicographically.

1, 1, 2, 2, 2, 1, 1, 2, 3, 1, 3, 1, 3, 2, 2, 1, 3, 2, 3, 2, 3, 1, 3, 3, 1, 3, 1, 2, 3, 2, 3, 2, 1, 1, 2, 3, 4, 1, 2, 4, 1, 2, 4, 3, 1, 3, 2, 4, 1, 3, 4, 1, 3, 4, 2, 1, 4, 1, 4, 2, 1, 4, 2, 3, 1, 4, 3, 1, 4, 3, 2, 2, 1, 3, 4, 2, 1, 4, 2, 1, 4, 3, 2, 3, 1, 4, 2

Offset

1,3

Comments

There are A001339(n - 1) sequences with a maximum value of n.

Conjecture: the sum of the sum of all sequences with a maximum value of n is given by A281912(n).

Links

Peter Kagey, Table of n, a(n) for n = 1..9786 (all sequences with maximum <= 6.)

Example

Maximum value 1:
[1],
Maximum value 2:
[1,2],
[2],
[2,1],
Maximum value 3:
[1,2,3],
[1,3],
[1,3,2],
[2,1,3],
[2,3],
[2,3,1],
[3],
[3,1],
[3,1,2],
[3,2],
[3,2,1]

Mathematica

Table[Map[ToExpression /@ StringPartition[#, 1, 1] &, Sort[Map[StringJoin, Join @@ Map[Permutations, DeleteCases[Rest@ Subsets[ToString /@ Range@ k], _?(FreeQ[#, ToString@ k] &)]]]]], {k, 4}] // Flatten (* Michael De Vlieger, Oct 15 2020 *)

Crossrefs

Cf. A001339, A026791, A228369, A281912.

Sequence in context: A238890 A266968 A237593 * A243847 A245421 A134143

Adjacent sequences: A338166 A338167 A338168 * A338170 A338171 A338172

Keyword

nonn,tabf

Author

Peter Kagey, Oct 14 2020

Status

approved