A338169 - OEIS

%I #19 Oct 16 2020 02:03:17

%S 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,

%T 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,

%U 4,3,2,2,1,3,4,2,1,4,2,1,4,3,2,3,1,4,2

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

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

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

%H Peter Kagey, <a href="/A338169/b338169.txt">Table of n, a(n) for n = 1..9786</a> (all sequences with maximum <= 6.)

%e Maximum value 1:

%e [1],

%e Maximum value 2:

%e [1,2],

%e [2],

%e [2,1],

%e Maximum value 3:

%e [1,2,3],

%e [1,3],

%e [1,3,2],

%e [2,1,3],

%e [2,3],

%e [2,3,1],

%e [3],

%e [3,1],

%e [3,1,2],

%e [3,2],

%e [3,2,1]

%t 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 *)

%Y Cf. A001339, A026791, A228369, A281912.

%K nonn,tabf

%O 1,3

%A _Peter Kagey_, Oct 14 2020