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.

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, 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, 2, 1, 3, 1, 1, 3, 2, 1, 1, 2, 3, 1, 1, 2, 2, 1, 1, 1, 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,
132,123,122,112,
1432,1423,1342,1332,1324,1323,1322,1243,1234,1233,1232,1223,1222,1213,1132,1123,1122,1112.

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[Reverse@normseqs@n, LyndonQ], {n, 5}]

Crossrefs

Cf. A000670, A019536, A060223, A095684, A185700, A281013, A294859, A296372, A296656, A296818, A296975-A296978.

Sequence in context: A240474 A023510 A005678 * A182321 A285731 A114905

Adjacent sequences: A296973 A296974 A296975 * A296977 A296978 A296979

Keyword

nonn,tabf

Author

Gus Wiseman, Dec 22 2017

Status

approved