A317718 Number of uniform relatively prime rooted trees with n nodes.

1, 1, 2, 4, 7, 13, 27, 55, 125, 278, 650, 1510, 3624, 8655, 21017, 51212, 125857, 310581, 770767, 1920226

Offset: 1

Author

Gus Wiseman, Aug 05 2018

Keywords

• nonn
• more

Comments

An unlabeled rooted tree is uniform and relatively prime iff either it is a single node or a single node with a single uniform relatively prime branch, or the branches of the root have empty intersection (relatively prime) and equal multiplicities (uniform) and are themselves uniform relatively prime trees.

Examples

			The a(6) = 13 uniform relatively prime rooted trees:
  (((((o)))))
  ((((oo))))
  (((o(o))))
  (((ooo)))
  ((o((o))))
  ((o(oo)))
  ((oooo))
  (o(((o))))
  (o((oo)))
  (o(o(o)))
  (o(ooo))
  ((o)((o)))
  (ooooo)
		

Links

• A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp. 1-12.

Crossrefs

Cf. A000081, A001190, A004111, A072774, A301700, A317588.

Cf. A317705, A317707, A317708, A317709, A317710, A317711, A317712, A317717.

Programs

Mathematica

purt[n_]:=purt[n]=If[n==1,{{}},Join@@Table[Select[Union[Sort/@Tuples[purt/@ptn]],Or[Length[#]==1,And[SameQ@@Length/@Split[#],Intersection@@#=={}]]&],{ptn,IntegerPartitions[n-1]}]];
Table[Length[purt[n]],{n,20}]