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

1,2

Links

Table of n, a(n) for n=1..15.

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

Cf. A328121, A328122, A328126.

Sequence in context: A346187 A012234 A012141 * A110553 A330360 A078326

Adjacent sequences: A328120 A328121 A328122 * A328124 A328125 A328126

Keyword

nonn

Author

Mathilde Bouvel, Oct 04 2019

Extensions

Name clarified by Mathilde Bouvel, Feb 03 2020

Status

approved