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 A317852 Number of plane trees with n nodes where the sequence of branches directly under any given node is aperiodic, meaning its cyclic permutations are all different. 4
 1, 1, 1, 3, 8, 26, 76, 247, 783, 2565, 8447, 28256, 95168, 323720, 1108415, 3821144, 13246307, 46158480, 161574043, 567925140, 2003653016, 7092953340, 25186731980, 89690452750, 320221033370, 1146028762599, 4110596336036, 14774346783745, 53203889807764, 191934931634880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Also the number of plane trees with n nodes where the sequence of branches directly under any given node has relatively prime run-lengths. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 EXAMPLE The a(5) = 8 locally aperiodic plane trees:   ((((o)))),   (((o)o)), ((o(o))), (((o))o), (o((o))),   ((o)oo), (o(o)o), (oo(o)). The a(6) = 26 locally aperiodic plane trees:   (((((o)))))  ((((o)o)))  (((o)oo))  ((o)ooo)                (((o(o))))  ((o(o)o))  (o(o)oo)                ((((o))o))  ((oo(o)))  (oo(o)o)                ((o((o))))  (((o)o)o)  (ooo(o))                ((((o)))o)  ((o(o))o)                (o(((o))))  (o((o)o))                (((o))(o))  (o(o(o)))                ((o)((o)))  (((o))oo)                            (o((o))o)                            (oo((o)))                            ((o)(o)o)                            ((o)o(o))                            (o(o)(o)) MATHEMATICA aperQ[q_]:=Array[RotateRight[q, #]&, Length[q], 1, UnsameQ]; aperplane[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[aperplane/@c], aperQ], {c, Join@@Permutations/@IntegerPartitions[n-1]}]]; Table[Length[aperplane[n]], {n, 10}] PROG (PARI) Tfm(p, n)={sum(d=1, n, moebius(d)*(subst(1/(1+O(x*x^(n\d))-p), x, x^d)-1))} seq(n)={my(p=O(1)); for(i=1, n, p=1+Tfm(x*p, i)); Vec(p)} \\ Andrew Howroyd, Feb 08 2020 CROSSREFS Cf. A000108, A000837, A007853, A032171, A032200, A254040, A301700, A303386, A303431, A304173, A304175, A317708, A317852. Sequence in context: A009452 A206141 A281972 * A306485 A148801 A131910 Adjacent sequences:  A317849 A317850 A317851 * A317853 A317854 A317855 KEYWORD nonn AUTHOR Gus Wiseman, Sep 05 2018 EXTENSIONS a(16)-a(17) from Robert Price, Sep 15 2018 Terms a(18) and beyond from Andrew Howroyd, Feb 08 2020 STATUS approved

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Last modified April 10 11:35 EDT 2021. Contains 342845 sequences. (Running on oeis4.)