A319271 Number of series-reduced locally non-intersecting aperiodic rooted trees with n nodes.

1, 1, 0, 1, 1, 3, 3, 9, 12, 27, 42, 91, 151, 312, 550, 1099, 2026, 3999, 7527, 14804, 28336, 55641, 107737, 211851, 413508, 814971, 1600512, 3162761, 6241234

Offset

1,6

Comments

A rooted tree is series-reduced if every non-leaf node has at least two branches, and aperiodic if the multiplicities in the multiset of branches directly under any given node are relatively prime, and locally non-intersecting if the branches directly under any given node with more than one branch have empty intersection.

Links

Table of n, a(n) for n=1..29.

Example

The a(8) = 9 rooted trees:
  (o(o(o(o))))
  (o(o(o)(o)))
  (o(ooo(o)))
  (oo(oo(o)))
  (o(o)(o(o)))
  (ooo(o(o)))
  (o(o)(o)(o))
  (ooo(o)(o))
  (ooooo(o))

Mathematica

btrut[n_]:=btrut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[btrut/@c]]]/@IntegerPartitions[n-1], And[Intersection@@#=={}, GCD@@Length/@Split[#]==1]&]];
Table[Length[btrut[n]], {n, 30}]

Crossrefs

Cf. A000081, A000837, A007562, A289509, A301700, A303431, A316470, A316473, A316475, A316495, A319270.

Sequence in context: A166720 A363129 A325243 * A066314 A083336 A225436

Adjacent sequences: A319268 A319269 A319270 * A319272 A319273 A319274

Keyword

nonn,more

Author

Gus Wiseman, Sep 16 2018

Status

approved