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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 6 11:37 EDT 2022. Contains 355110 sequences. (Running on oeis4.)