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A294859 Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in lexicographic order. 12
1, 2, 1, 2, 3, 1, 1, 2, 1, 3, 4, 1, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 4, 2, 3, 5, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 4, 1, 2, 3, 1, 3, 2, 1, 5, 2, 4, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 1, 4, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 3, 2, 1 (list; graph; refs; listen; history; text; internal format)
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),

(12),(3),

(112),(13),(4),

(1112),(113),(122),(14),(23),(5),

(11112),(1113),(1122),(114),(123),(132),(15),(24),(6),

(111112),(11113),(11122),(1114),(11212),(1123),(1132),(115),(1213),(1222),(124),(133),(142),(16),(223),(25),(34),(7).

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[{#1, #2}]]&], {n, 7}]

CROSSREFS

Cf. A000740, A001037, A001045, A008965, A059966, A060223, A066099, A101211, A102659, A124734, A185700, A228369, A281013, A296302, A296373, A296656.

Sequence in context: A238157 A272210 A273132 * A145782 A131797 A145727

Adjacent sequences:  A294856 A294857 A294858 * A294860 A294861 A294862

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Dec 18 2017

STATUS

approved

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Last modified July 13 08:26 EDT 2020. Contains 335685 sequences. (Running on oeis4.)