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 A319271 Number of series-reduced locally non-intersecting aperiodic rooted trees with n nodes. 2
 1, 1, 0, 1, 1, 3, 3, 9, 12, 27, 42, 91, 151, 312, 550, 1099, 2026, 3999, 7527, 14804, 28336, 55641, 107737, 211851, 413508, 814971, 1600512, 3162761, 6241234 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS A rooted tree is series-reduced if every non-leaf node has at least two branches, and aperiodic if the multiplicities in the multiset of branches directly under any given node are relatively prime, and locally non-intersecting if the branches directly under any given node with more than one branch have empty intersection. LINKS EXAMPLE The a(8) = 9 rooted trees:   (o(o(o(o))))   (o(o(o)(o)))   (o(ooo(o)))   (oo(oo(o)))   (o(o)(o(o)))   (ooo(o(o)))   (o(o)(o)(o))   (ooo(o)(o))   (ooooo(o)) MATHEMATICA btrut[n_]:=btrut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[btrut/@c]]]/@IntegerPartitions[n-1], And[Intersection@@#=={}, GCD@@Length/@Split[#]==1]&]]; Table[Length[btrut[n]], {n, 30}] CROSSREFS Cf. A000081, A000837, A007562, A289509, A301700, A303431, A316470, A316473, A316475, A316495, A319270. Sequence in context: A045810 A166720 A325243 * A066314 A083336 A225436 Adjacent sequences:  A319268 A319269 A319270 * A319272 A319273 A319274 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 16 2018 STATUS approved

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Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)