A317708 Number of aperiodic relatively prime trees with n nodes.

1, 1, 1, 2, 4, 10, 20, 48, 108, 255, 595, 1435, 3434, 8372, 20419, 50289, 124289, 309122, 771508, 1934462

Offset

1,4

Comments

An unlabeled rooted tree is aperiodic and relatively prime iff either it is a single node or a single node with a single aperiodic relatively prime branch, or the branches directly under any given node have empty intersection (relatively prime) and also have relatively prime multiplicities (aperiodic) and are themselves aperiodic relatively prime trees.

Links

Table of n, a(n) for n=1..20.

Gus Wiseman, All 48 aperiodic relatively prime trees with 8 nodes.

Example

The a(6) = 10 aperiodic relatively prime trees:
  (((((o)))))
  (((o(o))))
  ((o((o))))
  ((oo(o)))
  (o(((o))))
  (o(o(o)))
  ((o)((o)))
  (oo((o)))
  (o(o)(o))
  (ooo(o))

Mathematica

rurt[n_]:=If[n==1, {{}}, Join@@Table[Select[Union[Sort/@Tuples[rurt/@ptn]], Or[Length[#]==1, And[Intersection@@#=={}, GCD@@Length/@Split[#]==1]]&], {ptn, IntegerPartitions[n-1]}]];
Table[Length[rurt[n]], {n, 10}]

Crossrefs

Cf. A000081, A001190, A004111, A301700, A303431, A316501, A316500.

Cf. A317705, A317707, A317709, A317710, A317711, A317712.

Sequence in context: A232466 A003407 A151523 * A265264 A026395 A247630

Adjacent sequences: A317705 A317706 A317707 * A317709 A317710 A317711

Keyword

nonn,more

Author

Gus Wiseman, Aug 05 2018

Status

approved