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A304173 Number of rooted plane trees where every branch that has a predecessor (a branch directly to its left and emanating from the same root) has at least as many leaves as its predecessor. 5
1, 1, 2, 5, 13, 34, 90, 242, 660, 1822, 5085, 14333, 40759, 116817 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..14.

EXAMPLE

The a(5) = 13 plane trees:

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

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

  ((o)oo), (o(o)o), (oo(o)),

  (oooo).

Missing from this list is ((oo)o).

MATHEMATICA

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

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

CROSSREFS

Cf. A000081, A000108, A001003, A001006, A003238, A007853, A126120, A291442, A291443, A304175.

Sequence in context: A114173 A238435 A023425 * A217896 A090827 A109192

Adjacent sequences:  A304170 A304171 A304172 * A304174 A304175 A304176

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 16 2018

STATUS

approved

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Last modified March 19 15:02 EDT 2019. Contains 321330 sequences. (Running on oeis4.)