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A328123
Number of unrooted level-2 phylogenetic networks with (n+1) labeled leaves, when multiple (i.e. parallel) edges are allowed.
5
1, 9, 282, 14697, 1071750, 100467405, 11509922970, 1558302613245, 243426592473750, 43095781327975425, 8527098853816839450, 1864790504534293823025, 446647359698685492697350, 116281255808439040209815925, 32694665144001284972518220250
OFFSET
1,2
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.
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.
EXAMPLE
a(3) = 282 is the number of unrooted level-2 phylogenetic networks with 4 labeled leaves.
MAPLE
# see links section
CROSSREFS
KEYWORD
nonn
AUTHOR
Mathilde Bouvel, Oct 04 2019
EXTENSIONS
Name clarified by Mathilde Bouvel, Feb 03 2020
STATUS
approved