A224917 Stable k-tree numbers.

1, 1, 1, 2, 5, 15, 64, 342, 2344, 19137, 181204, 1927017, 22652805, 290392448, 4022276630, 59749492128, 946174967813, 15892939156209

Offset: 0

Author

Ira M. Gessel, Apr 19 2013

Keywords

• nonn
• more

Comments

a(n) is the number of unlabeled k-trees with n+k vertices for all k >= n-2.

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

Links

• Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
• A. Gainer-Dewar, Γ-species and the enumeration of k-trees, Electron. J. Combin. 19, no. 4, (2012), P45.
• I. M. Gessel and A. Gainer-Dewar, Counting unlabeled k-trees, arXiv:1309.1429 [math.CO], 2013-2014.
• I. M. Gessel and A. Gainer-Dewar, Counting unlabeled k-trees, J. Combin. Theory Ser. A 126 (2014), 177-193.

Crossrefs

Cf. A000055 (unlabeled trees), A054581 (unlabeled 2-trees), A078792 (unlabeled 3-trees), A078793 (unlabeled 4-trees), A201702 (unlabeled 5-trees), A202037 (unlabeled 6-trees).