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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 (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

Table of n, a(n) for n=1..17.

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}]

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,more

AUTHOR

Gus Wiseman, Sep 05 2018

EXTENSIONS

a(16)-a(17) from Robert Price, Sep 15 2018

STATUS

approved

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Last modified March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)