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Number of transitive rooted trees with n nodes.
82

%I #21 Dec 17 2023 03:09:00

%S 1,1,1,2,3,5,8,13,21,34,55,88,143,229,370,592,955,1527,2457,3929,6304,

%T 10081

%N Number of transitive rooted trees with n nodes.

%C A rooted tree is transitive if every proper terminal subtree is also a branch of the root. First differs from A206139 at a(13) = 143.

%H Robert P. P. McKone, <a href="/A290689/a290689.txt">The transitive rooted tree with n=1 to n=22 nodes</a>.

%e The a(7) = 8 trees are: (o(oooo)), (oo(ooo)), (o(o)((o))), (o(o)(oo)), (ooo(oo)), (oo(o)(o)), (oooo(o)), (oooooo).

%t nn=18;

%t rtall[n_]:=If[n===1,{{}},Module[{cas},Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])]]];

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

%Y Cf. A000081, A004111, A279861, A290822.

%K nonn,more

%O 1,4

%A _Gus Wiseman_, Oct 19 2017

%E a(20) from _Robert Price_, Sep 13 2018

%E a(21)-a(22) from _Robert P. P. McKone_, Dec 16 2023