A319378 Number of plane trees with n nodes where the sequence of branches directly under any given node with at least two branches has empty intersection.

1, 1, 2, 5, 13, 39, 118, 375, 1225, 4079, 13794, 47287, 163962, 573717, 2023800

Offset

1,3

Links

Table of n, a(n) for n=1..15.

Example

The a(5) = 13 locally nonintersecting plane trees:
  ((((o))))  (((oo)))  ((ooo))  (oooo)
             (((o)o))  ((oo)o)
             ((o(o)))  (o(oo))
             (((o))o)  ((o)oo)
             (o((o)))  (o(o)o)
                       (oo(o))

Mathematica

monplane[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[monplane/@c], Or[Length[#]==1, Intersection@@#=={}]&], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[monplane[n]], {n, 10}]

Crossrefs

Cf. A000081, A000108, A001003, A005043, A007562, A118376, A143363, A316470, A319122, A319379, A319380, A319381, A319436.

Sequence in context: A000800 A149860 A006823 * A151446 A239106 A022894

Adjacent sequences: A319375 A319376 A319377 * A319379 A319380 A319381

Keyword

nonn,more

Author

Gus Wiseman, Sep 17 2018

Status

approved