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A294859 Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in lexicographic order.

%I A294859 #22 Dec 19 2017 02:37:33
%S A294859 1,2,1,2,3,1,1,2,1,3,4,1,1,1,2,1,1,3,1,2,2,1,4,2,3,5,1,1,1,1,2,1,1,1,
%T A294859 3,1,1,2,2,1,1,4,1,2,3,1,3,2,1,5,2,4,6,1,1,1,1,1,2,1,1,1,1,3,1,1,1,2,
%U A294859 2,1,1,1,4,1,1,2,1,2,1,1,2,3,1,1,3,2,1
%N A294859 Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in lexicographic order.
%F A294859 Row n is a concatenation of A059966(n) Lyndon words with total length A000740(n).
%e A294859 Triangle of Lyndon compositions begins:
%e A294859 (1),
%e A294859 (2),
%e A294859 (12),(3),
%e A294859 (112),(13),(4),
%e A294859 (1112),(113),(122),(14),(23),(5),
%e A294859 (11112),(1113),(1122),(114),(123),(132),(15),(24),(6),
%e A294859 (111112),(11113),(11122),(1114),(11212),(1123),(1132),(115),(1213),(1222),(124),(133),(142),(16),(223),(25),(34),(7).
%t A294859 LyndonQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And]&&Array[RotateRight[q,#]&,Length[q],1,UnsameQ];
%t A294859 Table[Sort[Select[Join@@Permutations/@IntegerPartitions[n],LyndonQ],OrderedQ[PadRight[{#1,#2}]]&],{n,7}]
%Y A294859 Cf. A000740, A001037, A001045, A008965, A059966, A060223, A066099, A101211, A102659, A124734, A185700, A228369, A281013, A296302, A296373, A296656.
%K A294859 nonn,tabf
%O A294859 1,2
%A A294859 _Gus Wiseman_, Dec 18 2017