A391694 Number of distinct automorphism group orders among unlabeled trees with n vertices.

1, 1, 1, 2, 2, 4, 8, 11, 15, 18, 25, 36, 47, 60, 77, 97, 119, 150, 181, 223, 273, 335, 406, 487, 590

Offset

1,4

Comments

Let T_n be the set of all unlabeled trees on n vertices. For each T in T_n, let Aut(T) denote its automorphism group. Then a(n) = | { |Aut(T)| : T in T_n } |.

Links

Table of n, a(n) for n=1..25.

Igor Blokhin, Graph Theory, Python repository.

Example

For n = 5 there are three unlabeled trees. One tree has automorphism group of order 24, and two trees have automorphism groups of order 2. Hence the distinct orders are {2, 24}, and a(5) = 2.

Crossrefs

Cf. A000055.

Sequence in context: A050047 A056381 A245597 * A324039 A019463 A152763

Adjacent sequences: A391691 A391692 A391693 * A391695 A391696 A391697

Keyword

nonn,hard,more

Author

Igor Blokhin, Feb 21 2026

Extensions

a(21)-a(25) from Sean A. Irvine, Feb 25 2026

Status

approved