A290667 Number of asymmetric equicolorable (unrooted) trees with 2*n vertices.

0, 0, 0, 1, 4, 19, 84, 378, 1727, 8126, 39055, 191902, 960681

Offset

1,5

Comments

Any tree with 2n vertices is a bipartite graph with s vertices in one part and t vertices in the other part, where s <= t and s + t = 2n. We count trees with s = t = n, and which are asymmetric, that is, their only automorphism is the identity automorphism. These are also called identity trees.

References

R. C. Read and R. J. Wilson, Atlas of Graphs, Oxford Science Publications, Clarendon Press, OUP, 2004.

Links

Table of n, a(n) for n=1..13.

F. Hüffner, tinygraph, software for generating integer sequences based on graph properties.

Austin Mohr, Unlabeled Trees.

Example

a(3) = 0 because there are six trees with 6 vertices, but only three of these have s = t = n = 3, and none of these three is asymmetric. The fourth term a(4) = 1 because there are nine trees with 8 vertices with s = t = n = 4 but only 1 is asymmetric, namely tree T46. See "Atlas of Graphs", page 65.

Crossrefs

Cf. A119856 (equicolorable trees with 2n vertices), A000220 (asymmetric trees with n vertices).

Sequence in context: A180146 A017962 A260746 * A357572 A291416 A192526

Adjacent sequences: A290664 A290665 A290666 * A290668 A290669 A290670

Keyword

nonn,more

Author

John P. McSorley, Aug 08 2017

Extensions

a(10)-a(13) added using tinygraph by Falk Hüffner, Jul 25 2019

Status

approved