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 A301700 Number of aperiodic rooted trees with n nodes. 43
 1, 1, 1, 2, 4, 10, 21, 52, 120, 290, 697, 1713, 4200, 10446, 26053, 65473, 165257, 419357, 1068239, 2732509, 7013242, 18059960, 46641983, 120790324, 313593621, 816046050, 2128101601, 5560829666, 14557746453, 38177226541, 100281484375, 263815322761, 695027102020 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS An unlabeled rooted tree is aperiodic if the multiset of branches of the root is an aperiodic multiset, meaning it has relatively prime multiplicities, and each branch is also aperiodic. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..500 EXAMPLE The a(6) = 10 aperiodic trees are (((((o))))), (((o(o)))), ((o((o)))), ((oo(o))), (o(((o)))), (o(o(o))), ((o)((o))), (oo((o))), (o(o)(o)), (ooo(o)). MATHEMATICA arut[n_]:=arut[n]=If[n===1, {{}}, Join@@Function[c, Select[Union[Sort/@Tuples[arut/@c]], GCD@@Length/@Split[#]===1&]]/@IntegerPartitions[n-1]]; Table[Length[arut[n]], {n, 20}] PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} MoebiusT(v)={vector(#v, n, sumdiv(n, d, moebius(n/d)*v[d]))} seq(n)={my(v=[1]); for(n=2, n, v=concat([1], MoebiusT(EulerT(v)))); v} \\ Andrew Howroyd, Sep 01 2018 CROSSREFS Cf. A000081, A000740, A000837, A001678, A003238, A004111, A007716, A007916, A100953, A276625, A284639, A290689, A298422, A303386, A303431. Sequence in context: A165136 A165137 A065023 * A123445 A104431 A130666 Adjacent sequences:  A301697 A301698 A301699 * A301701 A301702 A301703 KEYWORD nonn AUTHOR Gus Wiseman, Apr 23 2018 EXTENSIONS Terms a(21) and beyond from Andrew Howroyd, Sep 01 2018 STATUS approved

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Last modified April 21 04:01 EDT 2021. Contains 343146 sequences. (Running on oeis4.)