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 A317718 Number of uniform relatively prime rooted trees with n nodes. 11
 1, 1, 2, 4, 7, 13, 27, 55, 125, 278, 650, 1510, 3624, 8655, 21017, 51212, 125857, 310581, 770767, 1920226 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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. LINKS A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp. 1-12. EXAMPLE 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) 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}] CROSSREFS Cf. A000081, A001190, A004111, A072774, A301700, A317588. Cf. A317705, A317707, A317708, A317709, A317710, A317711, A317712, A317717. Sequence in context: A309050 A265580 A136408 * A103104 A103480 A024826 Adjacent sequences:  A317715 A317716 A317717 * A317719 A317720 A317721 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 05 2018 STATUS approved

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)