cp's OEIS Frontend

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

%I A317718 #11 Aug 05 2018 20:42:35
%S A317718 1,1,2,4,7,13,27,55,125,278,650,1510,3624,8655,21017,51212,125857,
%T A317718 310581,770767,1920226
%N A317718 Number of uniform relatively prime rooted trees with n nodes.
%C A317718 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.
%H A317718 A. David Christopher and M. Davamani Christober, <a href="http://emis.impa.br/EMIS/journals/GMN/yahoo_site_admin/assets/docs/1_GMN-2492-V13N2.77213831.pdf">Relatively Prime Uniform Partitions</a>, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp. 1-12.
%e A317718 The a(6) = 13 uniform relatively prime rooted trees:
%e A317718   (((((o)))))
%e A317718   ((((oo))))
%e A317718   (((o(o))))
%e A317718   (((ooo)))
%e A317718   ((o((o))))
%e A317718   ((o(oo)))
%e A317718   ((oooo))
%e A317718   (o(((o))))
%e A317718   (o((oo)))
%e A317718   (o(o(o)))
%e A317718   (o(ooo))
%e A317718   ((o)((o)))
%e A317718   (ooooo)
%t A317718 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]}]];
%t A317718 Table[Length[purt[n]],{n,20}]
%Y A317718 Cf. A000081, A001190, A004111, A072774, A301700, A317588.
%Y A317718 Cf. A317705, A317707, A317708, A317709, A317710, A317711, A317712, A317717.
%K A317718 nonn,more
%O A317718 1,3
%A A317718 _Gus Wiseman_, Aug 05 2018