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A316696
Number of lone-child-avoiding locally disjoint rooted trees whose leaves form an integer partition of n.
13
1, 2, 4, 11, 27, 80, 218, 654, 1923, 5924, 18310, 58176, 186341, 606814, 1993420, 6618160, 22134640
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.
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
Matula-Goebel numbers of locally disjoint rooted trees are A316495.
The case where all leaves are 1's is A316697.
Lone-child-avoiding locally disjoint rooted trees are A331680.
Sequence in context: A309886 A123441 A086441 * A319616 A148130 A350030
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