login
A316769
Number of series-reduced locally stable rooted trees with n unlabeled leaves.
0
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.
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}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 12 2018
EXTENSIONS
a(17)-a(19) from Robert Price, Sep 14 2018
STATUS
approved