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A296976 List of normal Lyndon sequences ordered first by length and then reverse-lexicographically, where a finite sequence is normal if it spans an initial interval of positive integers.

%I A296976 #6 Dec 26 2017 17:46:15
%S A296976 1,1,2,1,3,2,1,2,3,1,2,2,1,1,2,1,4,3,2,1,4,2,3,1,3,4,2,1,3,3,2,1,3,2,
%T A296976 4,1,3,2,3,1,3,2,2,1,2,4,3,1,2,3,4,1,2,3,3,1,2,3,2,1,2,2,3,1,2,2,2,1,
%U A296976 2,1,3,1,1,3,2,1,1,2,3,1,1,2,2,1,1,1,2
%N A296976 List of normal Lyndon sequences ordered first by length and then reverse-lexicographically, where a finite sequence is normal if it spans an initial interval of positive integers.
%C A296976 Row n is formed by A060223(n) sequences and has length A296975(n).
%e A296976 Triangle of normal Lyndon sequences begins:
%e A296976 1,
%e A296976 12,
%e A296976 132,123,122,112,
%e A296976 1432,1423,1342,1332,1324,1323,1322,1243,1234,1233,1232,1223,1222,1213,1132,1123,1122,1112.
%t A296976 LyndonQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And]&&Array[RotateRight[q,#]&,Length[q],1,UnsameQ];
%t A296976 normseqs[n_]:=Union@@Permutations/@Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1];
%t A296976 Table[Select[Reverse@normseqs@n,LyndonQ],{n,5}]
%Y A296976 Cf. A000670, A019536, A060223, A095684, A185700, A281013, A294859, A296372, A296656, A296818, A296975-A296978.
%K A296976 nonn,tabf
%O A296976 1,3
%A A296976 _Gus Wiseman_, Dec 22 2017