A078793 Number of unlabeled 4-trees on n vertices.

0, 0, 0, 1, 1, 1, 2, 5, 15, 64, 331, 2150, 15817, 127194, 1077639, 9466983, 85252938, 782238933, 7283470324, 68639621442, 653492361220, 6276834750665, 60759388837299, 592227182125701, 5808446697002391, 57289008242377068, 567939935463185078

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 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.
• P. Di Francesco, P. Zinn-Justin, and J.-B. Zuber, Determinant Formulae for some Tiling Problems and Application to Fully Packed Loops, arXiv:math-ph/0410002, 2004.
• 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=4 of A370770.

Cf. A036506 (labeled 4-trees).

Extensions

More terms from Andrew R. Gainer, Dec 03 2011