

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
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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[n1]];
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



