cp's OEIS Frontend

A307942 Number of evolutionary duplication-loss-histories of the complete binary species tree with 8 leaves.

%I A307942 #12 Jul 31 2019 11:12:33
%S A307942 8,148,3376,89390,2624872,82866636,2755019736,95135709027,
%T A307942 3380416782760,122798718575216,4539685792433848,170225552910292438,
%U A307942 6458330316575589176,247456381334355675220,9561546562984390785960,372141845574597078971490,14575950501012888889866120
%N A307942 Number of evolutionary duplication-loss-histories of the complete binary species tree with 8 leaves.
%C A307942 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.
%F A307942 G.f.: 1/2-(1/2)*sqrt(-5+6*v-6*u+6*t+4*z) where t = sqrt(1-4*z), u = sqrt(-5+6*t+4*z) and v = sqrt(1+6*u-6*t-4*z).
%e A307942 See A307941 (complete binary species tree with 4 leaves).
%o A307942 (PARI) z='z+O('z^20); my(t = sqrt(1-4*z), u = sqrt(-5+6*t+4*z), v = sqrt(1+6*u-6*t-4*z)); Vec(1/2-(1/2)*sqrt(-5+6*v-6*u+6*t+4*z)) \\ _Jianing Song_, Jul 29 2019
%Y A307942 Cf. A000108 (caterpillar/complete binary species tree with 1 leaf, ordinary binary trees).
%Y A307942 Cf. A307696, A307697, A307698, A307700 (caterpillar species tree with 2, 3, 4, 5 leaves).
%K A307942 nonn
%O A307942 1,1
%A A307942 _Cedric Chauve_, May 07 2019