A316500 Number of unlabeled rooted identity trees with n nodes in which the branches of any node with more than one branch have empty intersection.

1, 1, 1, 2, 3, 6, 11, 22, 46, 96, 205, 442, 976, 2146, 4789, 10719, 24202, 54841, 124967, 285724, 656011, 1510929, 3491151, 8088692, 18790084

Offset

1,4

Links

Table of n, a(n) for n=1..25.

Example

The a(7) = 11 rooted identity trees:
  ((((((o))))))
  ((((o(o)))))
  (((o((o)))))
  ((o(((o)))))
  ((o(o(o))))
  (((o)((o))))
  (o((((o)))))
  (o((o(o))))
  (o(o((o))))
  ((o)(((o))))
  (o(o)((o)))

Mathematica

strut[n_]:=strut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1], UnsameQ@@#&&Or[Length[#]==1, Intersection@@#=={}]&]];
Table[Length[strut[n]], {n, 20}]

Crossrefs

Cf. A000081, A004111, A007562, A078374, A289509, A316469, A316471, A316474, A316501, A316503.

Sequence in context: A096202 A036653 A318031 * A123769 A093304 A036590

Adjacent sequences: A316497 A316498 A316499 * A316501 A316502 A316503

Keyword

nonn,more

Author

Gus Wiseman, Jul 05 2018

Status

approved