A202037 Number of unlabeled 6-trees on n nodes.

0, 0, 0, 0, 0, 1, 1, 1, 2, 5, 15, 64, 342, 2344, 19090, 179562, 1878277, 21365403, 258965451, 3294561195, 43472906719, 589744428065, 8171396893523, 115094557122380, 1642269376265063, 23679803216530017, 344396036645439675, 5045351124912000756

Offset: 1

Author

Andrew R. Gainer, Dec 09 2011

Keywords

• nonn

Comments

A k-tree is recursively defined as follows: K_k is a k-tree and any k-tree on n+1 vertices is obtained by joining a vertex to a k-clique in a k-tree on n vertices.

References

• Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 328.

Links

• Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
• Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45. - From _N. J. A. Sloane_, Dec 15 2012

Crossrefs

Column k=6 of A370770.

Cf. A054581 (unlabeled 2-trees), A078792 (unlabeled 3-trees), A078793 (unlabeled 4-trees), A201702 (unlabeled 5-trees)