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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
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
KEYWORD
nonn,tabf
AUTHOR
Peter Kagey, Oct 14 2020
STATUS
approved