%I #5 Dec 19 2017 02:41:47
%S 1,2,3,1,2,4,1,3,1,1,2,5,2,3,1,4,1,2,2,1,1,3,1,1,1,2,6,2,4,1,5,1,3,2,
%T 1,2,3,1,1,4,1,1,2,2,1,1,1,3,1,1,1,1,2,7,3,4,2,5,2,2,3,1,6,1,4,2,1,3,
%U 3,1,2,4,1,2,2,2,1,2,1,3,1,1,5,1,1,3,2
%N Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in reverse-lexicographic order.
%F Row n is a concatenation of A059966(n) Lyndon words with total length A000740(n).
%e Triangle of Lyndon compositions begins:
%e (1),
%e (2),
%e (3),(12),
%e (4),(13),(112),
%e (5),(23),(14),(122),(113),(1112),
%e (6),(24),(15),(132),(123),(114),(1122),(1113),(11112),
%e (7),(34),(25),(223),(16),(142),(133),(124),(1222),(1213),(115),(1132),(1123),(11212),(1114),(11122),(11113),(111112).
%t LyndonQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And]&&Array[RotateRight[q,#]&,Length[q],1,UnsameQ];
%t Table[Sort[Select[Join@@Permutations/@IntegerPartitions[n],LyndonQ],OrderedQ[PadRight[{#2,#1}]]&],{n,7}]
%Y Cf. A000740, A001037, A001045, A008965, A059966, A060223, A066099, A101211, A102659, A124734, A185700, A228369, A281013, A294859, A296302, A296373.
%K nonn,tabf
%O 1,2
%A _Gus Wiseman_, Dec 18 2017