A296977 List of normal Lyndon sequences ordered first by length and then lexicographically, where a finite sequence is normal if it spans an initial interval of positive integers.

1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 3, 1, 3, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 1, 1, 3, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 3, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 4, 1, 2, 4, 3, 1, 3, 2, 2, 1, 3, 2, 3, 1, 3, 2, 4, 1, 3, 3, 2, 1, 3, 4, 2, 1, 4, 2, 3, 1, 4, 3, 2

Offset

1,3

Comments

Row n is formed by A060223(n) sequences and has length A296975(n).

Links

Table of n, a(n) for n=1..87.

Example

Triangle of normal Lyndon sequences begins:
1,
12,
112,122,123,132,
1112,1122,1123,1132,1213,1222,1223,1232,1233,1234,1243,1322,1323,1324,1332,1342,1423,1432.

Mathematica

LyndonQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]&&Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];
normseqs[n_]:=Union@@Permutations/@Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];
Table[Select[normseqs[n], LyndonQ], {n, 5}]

Crossrefs

Cf. A000670, A019536, A060223, A095684, A185700, A281013, A294859, A296372, A296656, A296818, A296975, A296976.

Sequence in context: A245077 A008676 A025893 * A025878 A143421 A137672

Adjacent sequences: A296974 A296975 A296976 * A296978 A296979 A296980

Keyword

nonn,tabf

Author

Gus Wiseman, Dec 22 2017

Status

approved