A328123 Number of unrooted level-2 phylogenetic networks with (n+1) labeled leaves, when multiple (i.e. parallel) edges are allowed.
1, 9, 282, 14697, 1071750, 100467405, 11509922970, 1558302613245, 243426592473750, 43095781327975425, 8527098853816839450, 1864790504534293823025, 446647359698685492697350, 116281255808439040209815925, 32694665144001284972518220250
Offset: 1
Keywords
Examples
a(3) = 282 is the number of unrooted level-2 phylogenetic networks with 4 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, Version 2, arXiv:1909.10460 [math.CO], 2019.
Programs
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Maple
# see links section
Formula
Bouvel, Gambette and Mansouri provide (among other results) a closed formula for a(n), an equation for the associated exponential generating function, and an asymptotic estimate of a(n). See their Section 6.
Extensions
Name clarified by Mathilde Bouvel, Feb 03 2020