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

Author

Peter Kagey, Oct 14 2020

Keywords

• nonn
• tabf

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).

Examples

			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]
		

Links

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

Crossrefs

Cf. A001339, A026791, A228369, A281912.

Programs

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 *)