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A224917
Stable k-tree numbers.
0
1, 1, 1, 2, 5, 15, 64, 342, 2344, 19137, 181204, 1927017, 22652805, 290392448, 4022276630, 59749492128, 946174967813, 15892939156209
OFFSET
0,4
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).
Sequence in context: A201702 A202037 A322754 * A274100 A166355 A031154
KEYWORD
nonn,more
AUTHOR
Ira M. Gessel, Apr 19 2013
STATUS
approved