A201702 Number of unlabeled 5-trees on n nodes.

0, 0, 0, 0, 1, 1, 1, 2, 5, 15, 64, 342, 2321, 18578, 168287, 1656209, 17288336, 188006362, 2105867058, 24108331027, 280638347609, 3310098377912, 39462525169310, 474697793413215, 5754095507495584, 70216415130786725, 861924378411516159, 10636562125193377459

Offset: 1

Author

Andrew R. Gainer, Dec 03 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
• Eric Weisstein's World of Mathematics, k-Tree

Crossrefs

Column k=5 of A370770.

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