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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 (list; graph; refs; listen; history; text; internal format)
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[n-1], 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

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Last modified January 23 22:16 EST 2020. Contains 331177 sequences. (Running on oeis4.)