A316501 Number of unlabeled rooted trees with n nodes in which the branches of any node with more than one distinct branch have empty intersection.

1, 1, 2, 4, 9, 19, 45, 103, 250, 611, 1528, 3853, 9875, 25481, 66382, 174085, 459541, 1219462

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Example

The a(6) = 19 rooted trees:
  (((((o)))))
  ((((oo))))
  (((o(o))))
  (((ooo)))
  ((o((o))))
  ((o(oo)))
  (((o)(o)))
  ((oo(o)))
  ((oooo))
  (o(((o))))
  (o((oo)))
  (o(o(o)))
  (o(ooo))
  ((o)((o)))
  (oo((o)))
  (oo(oo))
  (o(o)(o))
  (ooo(o))
  (ooooo)

Mathematica

strut[n_]:=strut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1], Or[Length[Union[#]]==1, Intersection@@#=={}]&]];
Table[Length[strut[n]], {n, 15}]

Crossrefs

Cf. A000081, A007562, A289509, A302796, A316470, A316473, A316475, A316500, A316502.

Sequence in context: A084083 A036611 A316473 * A036612 A291648 A036613

Adjacent sequences: A316498 A316499 A316500 * A316502 A316503 A316504

Keyword

nonn,more

Author

Gus Wiseman, Jul 05 2018

Status

approved