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A316768
Number of series-reduced locally stable rooted trees whose leaves form an integer partition of n.
1
1, 2, 4, 11, 29, 91, 284, 950, 3235, 11336, 40370, 146095, 534774, 1977891, 7377235, 27719883
OFFSET
1,2
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 submultiset of any other branch of the same root.
EXAMPLE
The a(5) = 29 trees:
5,
(14),
(23),
(1(13)), (3(11)), (113),
(1(22)), (2(12)), (122),
(1(1(12))), (1(2(11))), (1(112)), (2(1(11))), (2(111)), ((11)(12)), (11(12)), (12(11)), (1112),
(1(1(1(11)))), (1(1(111))), (1((11)(11))), (1(11(11))), (1(1111)), ((11)(1(11))), (11(1(11))), (11(111)), (1(11)(11)), (111(11)), (11111).
Missing from this list but counted by A141268 is ((11)(111)).
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]=Prepend[Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]], stableQ], {ptn, Rest[IntegerPartitions[n]]}], {n}];
Table[Length[nms[n]], {n, 10}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 12 2018
EXTENSIONS
a(15)-a(16) from Robert Price, Sep 16 2018
STATUS
approved