A328121 Number of unrooted level-1 phylogenetic networks (also called galled trees) with (n+1) labeled leaves.
1, 2, 15, 192, 3450, 79740, 2252880, 75227040, 2898481320, 126570502800, 6177380517000, 333231084648000, 19687828831070400, 1264341183311606400, 87691200344603856000, 6532556443068591936000, 520205544912884502672000, 44098092640676115673632000, 3964782594938523231457584000
Offset: 1
Keywords
Examples
a(4) = 192 is the number of unrooted level-1 phylogenetic networks with 5 labeled leaves
Links
- Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, Maple worksheet
- Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, Counting Phylogenetic Networks of level 1 and 2, arXiv:1909.10460 [math.CO], 2019.
- Charles Semple and Mike Steel, Unicyclic networks: compatibility and enumeration, Transactions on Computational Biology and Bioinformatics (3:1 pp.398--401), 2006.
Programs
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Maple
# see links section
Formula
Semple and Steele provide a summation formula for a(n) (see their Theorem 4).
Bouvel, Gambette and Mansouri provide (among other additional results) an equation for the associated exponential generating function, and an asymptotic estimate of a(n). See their Section 4.