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Number of recursively anti-transitive rooted trees with n nodes.
18

%I #6 Mar 18 2019 08:15:10

%S 1,1,2,3,6,11,26,52,119,266,618,1432,3402,8093,19505,47228,115244,

%T 282529,696388,1723400

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

%C An unlabeled rooted tree is recursively anti-transitive if no branch of a branch of a terminal subtree is a branch of the same subtree.

%e The a(1) = 1 through a(6) = 11 recursively 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)))) (oo((o)))

%e ((((oo))))

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

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

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

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

%t nallt[n_]:=Select[Union[Sort/@Join@@(Tuples[nallt/@#]&/@IntegerPartitions[n-1])],Intersection[Union@@#,#]=={}&];

%t Table[Length[nallt[n]],{n,10}]

%Y Cf. A000081, A290689, A301700, A304360, A306844, A317787, A318185.

%Y Cf. A324695, A324751, A324756, A324758, A324764, A324766, A324767, A324768.

%Y Cf. A324838, A324840, A324844.

%K nonn,more

%O 1,3

%A _Gus Wiseman_, Mar 17 2019