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 A358455 Number of recursively anti-transitive ordered rooted trees with n nodes. 3
 1, 1, 2, 4, 10, 26, 72, 206, 608, 1830, 5612, 17442, 54866, 174252, 558072, 1800098 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS We define an unlabeled ordered rooted tree to be recursively anti-transitive if no branch of a branch of a subtree is a branch of the same subtree farther to the left. LINKS Table of n, a(n) for n=1..16. EXAMPLE The a(1) = 1 through a(5) = 10 trees: o (o) (oo) (ooo) (oooo) ((o)) ((o)o) ((o)oo) ((oo)) ((oo)o) (((o))) ((ooo)) (((o))o) (((o)o)) (((oo))) ((o)(o)) (o((o))) ((((o)))) MATHEMATICA aot[n_]:=If[n==1, {{}}, Join@@Table[Tuples[aot/@c], {c, Join@@Permutations/@IntegerPartitions[n-1]}]]; Table[Length[Select[aot[n], FreeQ[#, {___, x_, ___, {___, x_, ___}, ___}]&]], {n, 10}] CROSSREFS The unordered version is A324765, ranked by A324766. The undirected version is A358456. A000108 counts ordered rooted trees, unordered A000081. A306844 counts anti-transitive rooted trees. A358453 counts transitive ordered trees, unordered A290689. Cf. A318185, A324695, A324751, A324756, A324758, A324764, A324767, A324768, A324838, A324840, A324844. Sequence in context: A154835 A049145 A102407 * A356832 A148097 A148098 Adjacent sequences: A358452 A358453 A358454 * A358456 A358457 A358458 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 18 2022 STATUS approved

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Last modified August 9 16:51 EDT 2024. Contains 375044 sequences. (Running on oeis4.)