cp's OEIS Frontend

A259115 Number of unrooted binary ordered tanglegrams of size n.

%I A259115 #32 Dec 29 2020 20:41:36
%S A259115 1,1,1,2,4,31,243,3532,62810,1390718,36080361,1076477512,36281518847,
%T A259115 1363869480379,56587508558171,2569141702825037,126714642738385906,
%U A259115 6747643861563535720,385875940575529343271,23588199955061659841248,1535037278334227258123709,105961521687913311720698169
%N A259115 Number of unrooted binary ordered tanglegrams of size n.
%C A259115 Binary tanglegrams are pairs of bifurcating (degree 3 internal node) trees with a bijection between the leaves of the trees. Two tanglegrams are isomorphic if there is an isomorphism between the trees that preserves the bijection. Unrooted means that the tanglegram is composed of unrooted trees, and ordered means that the trees are considered as an ordered pair.
%H A259115 Andrew Howroyd, <a href="/A259115/b259115.txt">Table of n, a(n) for n = 1..50</a>
%H A259115 S. C. Billey, M. Konvalinka, and F. A. Matsen IV, <a href="http://arxiv.org/abs/1507.04976">On the enumeration of tanglegrams and tangled chains</a>, arXiv:1507.04976 [math.CO], 2015.
%H A259115 Ira M. Gessel, <a href="http://arxiv.org/abs/1509.03867">Counting tanglegrams with species</a>, arXiv:1509.03867 [math.CO], (13-September-2015)
%H A259115 F. A. Matsen IV, S. C. Billey, D. A. Kas, and M. Konvalinka, <a href="http://arxiv.org/abs/1507.04784">Tanglegrams: a reduction tool for mathematical phylogenetics</a>, arXiv:1507.04784 [q-bio.PE], 2015.
%H A259115 Frederick A. Matsen, <a href="https://github.com/matsengrp/tangle">Sage/GAP4 Code for generating tanglegrams</a>
%o A259115 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A259115 rootedBinTrees(n)={my(v=vector(n)); v[1]=sv(1); for(n=2, n, v[n]=(sum(j=1, n-1, v[j]*v[n-j]) + if(n%2, 0, sRaiseCI(v[n/2], n/2, 2)))/2); x*Ser(v)}
%o A259115 cycleIndexSeries(n)={my(g=rootedBinTrees(n), u = g + (sRaise(g,3) - g^3)/3); sCartProd(u,u)}
%o A259115 NumUnlabeledObjsSeq(cycleIndexSeries(12)) \\ _Andrew Howroyd_, Dec 24 2020
%Y A259115 Cf. A258620 (tanglegrams), A259114, A259116, A258486 (tangled chains), A258487, A258488, A258489.
%K A259115 nonn
%O A259115 1,4
%A A259115 _Frederick A. Matsen IV_, Jun 18 2015
%E A259115 More terms from _Ira M. Gessel_, Jul 19 2015
%E A259115 Terms a(15) and beyond from _Andrew Howroyd_, Dec 24 2020