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 A306844 Number of anti-transitive rooted trees with n nodes. 40

%I

%S 1,1,2,3,7,14,36,83,212,532,1379,3577,9444,25019,66943

%N Number of anti-transitive rooted trees with n nodes.

%C A rooted tree is anti-transitive if the subbranches are disjoint from the branches, i.e., no branch of a branch is a branch.

%H Gus Wiseman, <a href="/A306844/a306844.png">The a(7) = 36 anti-transitive rooted trees</a>.

%H Gus Wiseman, <a href="/A306844/a306844_1.png">The a(10) = 532 anti-transitive rooted trees</a>.

%e The a(1) = 1 through a(6) = 14 anti-transitive rooted trees:

%e o (o) (oo) (ooo) (oooo) (ooooo)

%e ((o)) ((oo)) ((ooo)) ((oooo))

%e (((o))) (((oo))) (((ooo)))

%e ((o)(o)) ((o)(oo))

%e ((o(o))) ((o(oo)))

%e (o((o))) ((oo(o)))

%e ((((o)))) (o((oo)))

%e (oo((o)))

%e ((((oo))))

%e (((o)(o)))

%e (((o(o))))

%e ((o((o))))

%e (o(((o))))

%e (((((o)))))

%t rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];

%t Table[Length[Select[rtall[n],Intersection[Union@@#,#]=={}&]],{n,10}]

%Y Cf. A276625, A279861, A279861, A290689, A290760, A304360.

%Y Cf. A324694, A324695, A324738, A324741, A324743, A324751, A324754, A324756, A324758, A324759, A324764.

%K nonn,more

%O 1,3

%A _Gus Wiseman_, Mar 13 2019

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Last modified May 27 21:12 EDT 2020. Contains 334671 sequences. (Running on oeis4.)