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A337114
Number of distinct node-partitions of n-vertex trees.
1
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
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
KEYWORD
nonn,more
AUTHOR
Gordon Hamilton, Aug 16 2020
EXTENSIONS
a(13)-a(24) from Bert Dobbelaere, Aug 25 2020
STATUS
approved