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A338169 A list of all finite sequences of distinct positive integers sorted by their maximum value, then lexicographically. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)