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Number of unlabeled 3-trees on n vertices.
5

%I #37 Mar 02 2024 11:59:34

%S 0,0,1,1,1,2,5,15,58,275,1505,9003,56931,372973,2506312,17165954,

%T 119398333,841244274,5993093551,43109340222,312747109787,

%U 2286190318744,16826338257708,124605344758149,927910207739261,6945172081954449,52225283886702922

%N Number of unlabeled 3-trees on n vertices.

%C 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.

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

%H Allan Bickle, <a href="https://doi.org/10.20429/tag.2024.000105">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.

%H Andrew Gainer-Dewar, <a href="https://doi.org/10.37236/2615">Gamma-Species and the Enumeration of k-Trees</a>, Electronic Journal of Combinatorics, Volume 19 (2012), #P45. - From _N. J. A. Sloane_, Dec 15 2012

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/k-Tree.html">k-Tree</a>.

%Y Column k=3 of A370770.

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

%K nonn

%O 1,6

%A _Gordon F. Royle_, Dec 05 2002

%E More terms from _Andrew R. Gainer_, Dec 03 2011