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A306844
Number of anti-transitive rooted trees with n nodes.
46
1, 1, 2, 3, 7, 14, 36, 83, 212, 532, 1379, 3577, 9444, 25019, 66943, 179994, 487031, 1323706, 3614622, 9907911
OFFSET
1,3
COMMENTS
A rooted tree is anti-transitive if the subbranches are disjoint from the branches, i.e., no branch of a branch is a branch.
EXAMPLE
The a(1) = 1 through a(6) = 14 anti-transitive rooted trees:
o (o) (oo) (ooo) (oooo) (ooooo)
((o)) ((oo)) ((ooo)) ((oooo))
(((o))) (((oo))) (((ooo)))
((o)(o)) ((o)(oo))
((o(o))) ((o(oo)))
(o((o))) ((oo(o)))
((((o)))) (o((oo)))
(oo((o)))
((((oo))))
(((o)(o)))
(((o(o))))
((o((o))))
(o(((o))))
(((((o)))))
MATHEMATICA
rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];
Table[Length[Select[rtall[n], Intersection[Union@@#, #]=={}&]], {n, 10}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 13 2019
EXTENSIONS
a(16)-a(20) from Jinyuan Wang, Jun 20 2020
STATUS
approved