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%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
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