OFFSET
1,3
COMMENTS
We define an unlabeled ordered rooted tree to be recursively bi-anti-transitive if there are no two branches of the same node such that one is a branch of the other.
EXAMPLE
The a(1) = 1 through a(6) = 17 trees:
o (o) (oo) (ooo) (oooo) (ooooo)
((o)) ((oo)) ((ooo)) ((oooo))
(((o))) (((o))o) (((o))oo)
(((oo))) (((oo))o)
((o)(o)) (((ooo)))
(o((o))) ((o)(oo))
((((o)))) ((oo)(o))
(o((o))o)
(o((oo)))
(oo((o)))
((((o)))o)
((((o))o))
((((oo))))
(((o)(o)))
((o((o))))
(o(((o))))
(((((o)))))
MATHEMATICA
aot[n_]:=If[n==1, {{}}, Join@@Table[Tuples[aot/@c], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[aot[n], FreeQ[#, {___, x_, ___, {___, x_, ___}, ___}|{___, {___, x_, ___}, ___, x_, ___}]&]], {n, 10}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 18 2022
STATUS
approved