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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 * A336320 A145782 A131797 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 February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)