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%I #6 Mar 18 2019 08:15:54
%S 1,1,2,3,5,7,14,23,46,85,165,313,625,1225,2459,4919,9928,20078,40926,
%T 83592
%N Number of fully recursively anti-transitive rooted trees with n nodes.
%C An unlabeled rooted tree is fully recursively anti-transitive if no proper terminal subtree of any terminal subtree is a branch of the larger subtree.
%H Gus Wiseman, <a href="/A324840/a324840.png">The a(8) = 23 fully recursively anti-transitive rooted trees</a>.
%H Gus Wiseman, <a href="/A324840/a324840_1.png">The a(9) = 46 fully recursively anti-transitive rooted trees</a>.
%H Gus Wiseman, <a href="/A324840/a324840_2.png">The a(10) = 85 fully recursively anti-transitive rooted trees</a>.
%e The a(1) = 1 through a(7) = 14 fully recursively anti-transitive rooted trees:
%e o (o) (oo) (ooo) (oooo) (ooooo) (oooooo)
%e ((o)) ((oo)) ((ooo)) ((oooo)) ((ooooo))
%e (((o))) (((oo))) (((ooo))) (((oooo)))
%e ((o)(o)) ((o)(oo)) ((o)(ooo))
%e ((((o)))) ((((oo)))) ((oo)(oo))
%e (((o)(o))) ((((ooo))))
%e (((((o))))) (((o))(oo))
%e (((o)(oo)))
%e ((o)((oo)))
%e ((o)(o)(o))
%e (((((oo)))))
%e ((((o)(o))))
%e (((o))((o)))
%e ((((((o))))))
%t dallt[n_]:=Select[Union[Sort/@Join@@(Tuples[dallt/@#]&/@IntegerPartitions[n-1])],Intersection[Union@@Rest[FixedPointList[Union@@#&,#]],#]=={}&];
%t Table[Length[dallt[n]],{n,10}]
%Y Cf. A000081, A279861, A290689, A304360, A306844, A318185.
%Y Cf. A324695, A324751, A324756, A324758, A324763, A324765, A324768, A324769, A324770.
%Y Cf. A324838, A324841, A324844, A324846.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Mar 17 2019
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