A316769 Number of series-reduced locally stable rooted trees with n unlabeled leaves.

1, 1, 2, 5, 11, 29, 74, 205, 578, 1683, 4978, 15000, 45672, 140600, 436421, 1364876, 4295403, 13594685, 43238514

Offset

1,3

Comments

A rooted tree is series-reduced if every non-leaf node has at least two branches. It is locally stable if no branch is a proper submultiset of any other branch of the same root.

Links

Table of n, a(n) for n=1..19.

Example

The a(5) = 11 trees:
  (o(o(o(oo))))
  (o(o(ooo)))
  (o((oo)(oo)))
  (o(oo(oo)))
  (o(oooo))
  ((oo)(o(oo)))
  (oo(o(oo)))
  (oo(ooo))
  (o(oo)(oo))
  (ooo(oo))
  (ooooo)
Missing from this list but counted by A000669 is ((oo)(ooo)).

Mathematica

submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]];
stableQ[u_]:=Apply[And, Outer[#1==#2||!submultisetQ[#1, #2]&&!submultisetQ[#2, #1]&, u, u, 1], {0, 1}];
nms[n_]:=nms[n]=If[n==1, {{1}}, Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]], stableQ], {ptn, Rest[IntegerPartitions[n]]}]];
Table[Length[nms[n]], {n, 12}]

Crossrefs

Cf. A000081, A000669, A001678, A141268, A316475, A316651, A316652, A316655.

Sequence in context: A117719 A355516 A359661 * A192785 A334578 A360810

Adjacent sequences: A316766 A316767 A316768 * A316770 A316771 A316772

Keyword

nonn,more

Author

Gus Wiseman, Jul 12 2018

Extensions

a(17)-a(19) from Robert Price, Sep 14 2018

Status

approved