A370770 Triangle read by rows: T(n,k) is the number of k-trees with n unlabeled nodes.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 6, 5, 2, 1, 1, 1, 1, 11, 12, 5, 2, 1, 1, 1, 1, 23, 39, 15, 5, 2, 1, 1, 1, 1, 47, 136, 58, 15, 5, 2, 1, 1, 1, 1, 106, 529, 275, 64, 15, 5, 2, 1, 1, 1, 1, 235, 2171, 1505, 331, 64, 15, 5, 2, 1, 1, 1
Offset: 0
Examples
Triangle begins: 1; 1, 1; 1, 1, 1; 1, 1, 1, 1; 1, 2, 1, 1, 1; 1, 3, 2, 1, 1, 1; 1, 6, 5, 2, 1, 1, 1; 1, 11, 12, 5, 2, 1, 1, 1; 1, 23, 39, 15, 5, 2, 1, 1, 1; 1, 47, 136, 58, 15, 5, 2, 1, 1, 1; 1, 106, 529, 275, 64, 15, 5, 2, 1, 1, 1; ...
Links
- Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
- Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (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.
- Andrew Howroyd, SageMath Program code (from Andrew Gainer-Dewar reference).