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%I #12 Jul 09 2019 13:16:41
%S 16,616,28832,1556780,93017264,5971377672,403667945712,28346017000314,
%T 2048467088599520,151362953286590792,11383212160213595696,
%U 868385902978402717696,67032303753464250574432,5225869642113491897295040,410865063418648682500317120
%N Number of evolutionary duplication-loss-histories of the complete binary species tree with 16 leaves.
%C 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.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a307/A307943.java">Java program</a> (github)
%F G.f.: 1/2-(1/2)*sqrt(1-6*v+6*w+6*u-6*t-4*z) where t = sqrt(1-4*z), u = sqrt(-5+6*t+4*z), v = sqrt(1+6*u-6*t-4*z) and w = sqrt(-5+6*v-6*u+6*t+4*z)
%e See A307941 (complete binary species tree with 4 leaves).
%Y Cf. A000108 (caterpillar/complete binary species tree with 1 leaf, ordinary binary trees).
%Y Cf. A307696, A307697, A307698, A307700 (caterpillar species tree with 2, 3, 4, 5 leaves).
%K nonn
%O 1,1
%A _Cedric Chauve_, May 07 2019
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