cp's OEIS Frontend

A316697 Number of series-reduced locally disjoint rooted trees with n unlabeled leaves.

%I A316697 #11 Dec 09 2024 19:46:47
%S A316697 1,1,2,5,10,24,49,112,241,548,1218,2839,6547,15572,37179,90555,222065,
%T A316697 552576,1384820,3506475,8936121,22941280
%N A316697 Number of series-reduced locally disjoint rooted trees with n unlabeled leaves.
%C A316697 A rooted tree is series-reduced if every non-leaf node has at least two branches. It is locally disjoint if no branch overlaps any other (unequal) branch of the same root.
%e A316697 The a(5) = 10 trees:
%e A316697   (o(o(o(oo))))
%e A316697   (o(o(ooo)))
%e A316697   (o((oo)(oo)))
%e A316697   (o(oo(oo)))
%e A316697   (o(oooo))
%e A316697   (oo(o(oo)))
%e A316697   (oo(ooo))
%e A316697   (o(oo)(oo))
%e A316697   (ooo(oo))
%e A316697   (ooooo)
%e A316697 Missing from this list but counted by A000669 are ((oo)(o(oo))) and ((oo)(ooo)).
%t A316697 disjointQ[u_]:=Apply[And,Outer[#1==#2||Intersection[#1,#2]=={}&,u,u,1],{0,1}];
%t A316697 nms[n_]:=nms[n]=If[n==1,{{1}},Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]],disjointQ],{ptn,Rest[IntegerPartitions[n]]}]];
%t A316697 Table[Length[nms[n]],{n,15}]
%Y A316697 Cf. A000081, A000669, A001678, A141268, A316471, A316471, A316475, A316495.
%K A316697 nonn,more
%O A316697 1,3
%A A316697 _Gus Wiseman_, Jul 10 2018
%E A316697 a(18)-a(22) from _Robert Price_, Sep 14 2018