A347414 Number of partitions of n which occur as the automorphism orbit sizes of a rooted forest of n vertices.

1, 2, 3, 5, 6, 11, 13, 21, 28, 38, 51, 73, 93, 124, 163, 212, 278, 352, 459, 572, 736, 914, 1187, 1434, 1838

Offset

1,2

Comments

Also, the number of partitions of n+1 which occur as the automorphism orbit sizes of a rooted tree of n+1 vertices, since the tree root is alone in its orbit and a tree without its root is a forest.

Links

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

Kevin Ryde, C program using Nauty to calculate terms

Example

For n=9, one of the partitions counted is 1+1+1+2+2+2 = 9 which is the orbit sizes of the following forest (and various other forests too):
  roots:       a       c       orbit: a  b  c  d  e  f
               |      / \      size:  1  1  1  2  2  2
  children:    b     e   e
              / \    |   |
             d   d   f   f

Crossrefs

Cf. A337114 (in free trees), A000041 (all partitions).

Sequence in context: A100883 A240303 A240218 * A317707 A329159 A350230

Adjacent sequences: A347411 A347412 A347413 * A347415 A347416 A347417

Keyword

nonn,more

Author

Kevin Ryde, Aug 31 2021

Status

approved