|
|
A319378
|
|
Number of plane trees with n nodes where the sequence of branches directly under any given node with at least two branches has empty intersection.
|
|
3
|
|
|
1, 1, 2, 5, 13, 39, 118, 375, 1225, 4079, 13794, 47287, 163962, 573717, 2023800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
EXAMPLE
|
The a(5) = 13 locally nonintersecting plane trees:
((((o)))) (((oo))) ((ooo)) (oooo)
(((o)o)) ((oo)o)
((o(o))) (o(oo))
(((o))o) ((o)oo)
(o((o))) (o(o)o)
(oo(o))
|
|
MATHEMATICA
|
monplane[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[monplane/@c], Or[Length[#]==1, Intersection@@#=={}]&], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[monplane[n]], {n, 10}]
|
|
CROSSREFS
|
Cf. A000081, A000108, A001003, A005043, A007562, A118376, A143363, A316470, A319122, A319379, A319380, A319381, A319436.
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|