A296656 Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in reverse-lexicographic order.

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, 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, 3, 1, 2, 4, 1, 2, 2, 2, 1, 2, 1, 3, 1, 1, 5, 1, 1, 3, 2

Offset

1,2

Links

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

Formula

Row n is a concatenation of A059966(n) Lyndon words with total length A000740(n).

Example

Triangle of Lyndon compositions begins:
(1),
(2),
(3),(12),
(4),(13),(112),
(5),(23),(14),(122),(113),(1112),
(6),(24),(15),(132),(123),(114),(1122),(1113),(11112),
(7),(34),(25),(223),(16),(142),(133),(124),(1222),(1213),(115),(1132),(1123),(11212),(1114),(11122),(11113),(111112).

Mathematica

LyndonQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]&&Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];
Table[Sort[Select[Join@@Permutations/@IntegerPartitions[n], LyndonQ], OrderedQ[PadRight[{#2, #1}]]&], {n, 7}]

Crossrefs

Cf. A000740, A001037, A001045, A008965, A059966, A060223, A066099, A101211, A102659, A124734, A185700, A228369, A281013, A294859, A296302, A296373.

Sequence in context: A088422 A100833 A097293 * A303945 A026793 A344089

Adjacent sequences: A296653 A296654 A296655 * A296657 A296658 A296659

Keyword

nonn,tabf

Author

Gus Wiseman, Dec 18 2017

Status

approved