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A304175 Number of leaf-balanced rooted plane trees with n nodes. 5
1, 1, 2, 5, 12, 27, 59, 128, 277, 597, 1280, 2730, 5794, 12248, 25836, 54508 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A rooted plane tree is leaf-balanced if every branch of the root has the same number of leaves, and every branch of the root is itself leaf-balanced.

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

The a(5) = 12 leaf-balanced plane trees:

  ((((o)))), (((oo))), (((o)o)), ((o(o))), ((ooo)),

  (((o))o), (o((o))), ((o)(o)),

  ((o)oo), (o(o)o), (oo(o)),

  (oooo).

Missing from this list are ((oo)o) and (o(oo)).

MATHEMATICA

lbplane[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[lbplane/@c], SameQ@@(Count[#, {}, {0, Infinity}]&/@#)&], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];

Table[Length[lbplane[n]], {n, 10}]

CROSSREFS

Cf. A000081, A000108, A001003, A001006, A003238, A007853, A126120, A291442, A291443, A304173.

Sequence in context: A083378 A116712 A000102 * A086589 A299270 A190171

Adjacent sequences:  A304172 A304173 A304174 * A304176 A304177 A304178

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 16 2018

STATUS

approved

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Last modified March 23 12:43 EDT 2019. Contains 321430 sequences. (Running on oeis4.)