

A307943


Number of evolutionary duplicationlosshistories of the complete binary species tree with 16 leaves.


1



16, 616, 28832, 1556780, 93017264, 5971377672, 403667945712, 28346017000314, 2048467088599520, 151362953286590792, 11383212160213595696, 868385902978402717696, 67032303753464250574432, 5225869642113491897295040, 410865063418648682500317120
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OFFSET

1,1


COMMENTS

An evolutionary history of size n is an ordered rooted (incomplete) binary tree with n leaves describing the evolution of a gene family of a species in phylogenomics. The complete binary species tree S of size k is a complete binary tree with k leaves. Any node of the history is associated to a unique node of S, where specifically every leaf is associated to a leaf of S. A history is created by the following process (note that intermediate trees in this process may not be valid histories): Start with a root node associated to the root of S. For a given tree in the growth process, choose a leaf and perform a duplication, speciation, or (speciation)loss event. A duplication event creates two children both associated to the same node as its parent. A speciation or (speciation)loss event can only occur if the node is associated to an internal node in S. In that case, a speciation event creates two children associated to the children of the node in S. A (speciation)loss event creates only a left or right child, associated to the left or right child in S, respectively.


LINKS

Table of n, a(n) for n=1..15.
Sean A. Irvine, Java program (github)


FORMULA

G.f.: 1/2(1/2)*sqrt(16*v+6*w+6*u6*t4*z) where t = sqrt(14*z), u = sqrt(5+6*t+4*z), v = sqrt(1+6*u6*t4*z) and w = sqrt(5+6*v6*u+6*t+4*z)


EXAMPLE

See A307941 (complete binary species tree with 4 leaves).


CROSSREFS

Cf. A000108 (caterpillar/complete binary species tree with 1 leaf, ordinary binary trees).
Cf. A307696, A307697, A307698, A307700 (caterpillar species tree with 2, 3, 4, 5 leaves).
Sequence in context: A222845 A187403 A265638 * A171210 A266129 A174336
Adjacent sequences: A307940 A307941 A307942 * A307944 A307945 A307946


KEYWORD

nonn


AUTHOR

Cedric Chauve, May 07 2019


STATUS

approved



