

A316795


Number of aperiodic rooted trees on n nodes with locally distinct multiplicities.


5



1, 1, 1, 1, 2, 5, 8, 17, 30, 55, 101, 194, 352, 663, 1227, 2275, 4225, 7877, 14600, 27158, 50414, 93666, 173972, 323286, 600353
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OFFSET

1,5


COMMENTS

An aperiodic rooted tree is an unlabeled rooted tree in which the multiplicities of branches under any given node are relatively prime. A rooted tree has locally distinct multiplicities if the multiset of branches under any given node has all distinct multiplicities.


LINKS

Table of n, a(n) for n=1..25.
Gus Wiseman, The a(9) = 30 aperiodic trees with locally distinct multiplicities.


EXAMPLE

The a(7) = 8 trees:
((((((o))))))
(((oo(o))))
((oo((o))))
((o(o)(o)))
((ooo(o)))
(oo(((o))))
(ooo((o)))
(oooo(o))


MATHEMATICA

strut[n_]:=strut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n1], And[UnsameQ@@Length/@Split[#], GCD@@Length/@Split[#]==1]&]];
Table[Length[strut[n]], {n, 15}]


CROSSREFS

Cf. A000081, A000837, A004111, A301700, A303431, A316793, A316794, A316796.
Sequence in context: A034445 A285459 A259580 * A054754 A054755 A093331
Adjacent sequences: A316792 A316793 A316794 * A316796 A316797 A316798


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jul 14 2018


STATUS

approved



