cp's OEIS Frontend

A317708 Number of aperiodic relatively prime trees with n nodes.

%I A317708 #8 Aug 05 2018 08:24:41
%S A317708 1,1,1,2,4,10,20,48,108,255,595,1435,3434,8372,20419,50289,124289,
%T A317708 309122,771508,1934462
%N A317708 Number of aperiodic relatively prime trees with n nodes.
%C A317708 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.
%H A317708 Gus Wiseman, <a href="/A317708/a317708.png">All 48 aperiodic relatively prime trees with 8 nodes.</a>
%e A317708 The a(6) = 10 aperiodic relatively prime trees:
%e A317708   (((((o)))))
%e A317708   (((o(o))))
%e A317708   ((o((o))))
%e A317708   ((oo(o)))
%e A317708   (o(((o))))
%e A317708   (o(o(o)))
%e A317708   ((o)((o)))
%e A317708   (oo((o)))
%e A317708   (o(o)(o))
%e A317708   (ooo(o))
%t A317708 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]}]];
%t A317708 Table[Length[rurt[n]],{n,10}]
%Y A317708 Cf. A000081, A001190, A004111, A301700, A303431, A316501, A316500.
%Y A317708 Cf. A317705, A317707, A317709, A317710, A317711, A317712.
%K A317708 nonn,more
%O A317708 1,4
%A A317708 _Gus Wiseman_, Aug 05 2018