OFFSET
1,2
COMMENTS
A rooted tree is lone-child-avoiding 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.
LINKS
EXAMPLE
The a(4) = 11 rooted trees:
4,
(13),
(22),
(1(12)), (2(11)), (112),
(1(1(11))), (1(111)), ((11)(11)), (11(11)), (1111).
MATHEMATICA
disjointQ[u_]:=Apply[And, Outer[#1==#2||Intersection[#1, #2]=={}&, u, u, 1], {0, 1}];
nms[n_]:=nms[n]=Prepend[Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]], disjointQ], {ptn, Rest[IntegerPartitions[n]]}], {n}];
Table[Length[nms[n]], {n, 10}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 10 2018
EXTENSIONS
a(16)-a(17) from Robert Price, Sep 16 2018
Terminology corrected by Gus Wiseman, Feb 06 2020
STATUS
approved