A078792 Number of unlabeled 3-trees on n vertices.

0, 0, 1, 1, 1, 2, 5, 15, 58, 275, 1505, 9003, 56931, 372973, 2506312, 17165954, 119398333, 841244274, 5993093551, 43109340222, 312747109787, 2286190318744, 16826338257708, 124605344758149, 927910207739261, 6945172081954449, 52225283886702922

Offset: 1

Author

Gordon F. Royle, Dec 05 2002

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 new 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=3 of A370770.

Cf. A036362 (labeled 3-trees), A054581 (unlabeled 2-trees).

Extensions

More terms from Andrew R. Gainer, Dec 03 2011