A328126 Number of rooted level-2 phylogenetic networks with n labeled leaves, when multiple (i.e. parallel) edges are allowed.
1, 24, 1935, 259098, 48547410, 11693494530, 3442245242940, 1197493950509640, 480665307600153900, 218657025956206794600, 111169169621733787779600, 62469471023839610046855000, 38446561750101105716524609200, 25719207873623040944564642044800, 18581469164514130166868945471102000
Offset: 1
Keywords
Examples
a(3) = 1935 is the number of rooted level-2 phylogenetic networks with 3 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
-
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 7.
Extensions
Name clarified by Mathilde Bouvel, Feb 03 2020