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A296656 Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in reverse-lexicographic order. 6
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 (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),
(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
Sequence in context: A088422 A100833 A097293 * A303945 A026793 A344089
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Dec 18 2017
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)