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Number of unlabeled 4-trees on n vertices.
6

%I #34 Mar 02 2024 11:59:12

%S 0,0,0,1,1,1,2,5,15,64,331,2150,15817,127194,1077639,9466983,85252938,

%T 782238933,7283470324,68639621442,653492361220,6276834750665,

%U 60759388837299,592227182125701,5808446697002391,57289008242377068,567939935463185078

%N Number of unlabeled 4-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 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 P. Di Francesco, P. Zinn-Justin, and J.-B. Zuber, <a href="https://arXiv.org/abs/math-ph/0410002">Determinant Formulae for some Tiling Problems and Application to Fully Packed Loops</a>, arXiv:math-ph/0410002, 2004.

%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=4 of A370770.

%Y Cf. A036506 (labeled 4-trees).

%K nonn

%O 1,7

%A _Gordon F. Royle_, Dec 05 2002

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