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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
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
Sequence in context: A238157 A272210 A273132 * A336320 A145782 A131797
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Dec 18 2017
STATUS
approved

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Last modified February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)