A337114 Number of distinct node-partitions of n-vertex trees.

1, 1, 1, 2, 3, 6, 9, 15, 19, 32, 36, 56, 70, 103, 122, 175, 210, 298, 349, 486, 569, 773, 912, 1237

Offset

1,4

Links

Table of n, a(n) for n=1..24.

Gordon Hamilton, Treefolk Tribes

Example

There are three node-partitions of 5-vertex trees. 1) The star graph has a unique central element four indistinguishable leaves. This corresponds to the 1-4 partition. 2) 5-vertices in a line has a unique central vertex. Both neighboring vertices are indistinguishable. The two leaves are indistinguishable. This corresponds to the 1,2,2 partition. 3) The remaining 5-vertex tree corresponds to the 1,1,1,2 partition.
Among the 12-vertex trees, there are many which share a node partition. For example there are four which share the node partition: 1,1,1,1,3,5 and seventy nine that share the node partition: 1,1,1,1,1,1,1,1,1,1,2. Of the seventy-seven partitions of 12 there are 21 that have no associated tree 77-a(12) = 77-56 = 21.

Crossrefs

Sequence in context: A303664 A190276 A113808 * A308870 A273371 A040040

Adjacent sequences: A337111 A337112 A337113 * A337115 A337116 A337117

Keyword

nonn,more

Author

Gordon Hamilton, Aug 16 2020

Extensions

a(13)-a(24) from Bert Dobbelaere, Aug 25 2020

Status

approved