A259115 Number of unrooted binary ordered tanglegrams of size n.

1, 1, 1, 2, 4, 31, 243, 3532, 62810, 1390718, 36080361, 1076477512, 36281518847, 1363869480379, 56587508558171, 2569141702825037, 126714642738385906, 6747643861563535720, 385875940575529343271, 23588199955061659841248, 1535037278334227258123709, 105961521687913311720698169

Offset: 1

Author

Frederick A. Matsen IV, Jun 18 2015

Keywords

• nonn

Comments

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.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• S. C. Billey, M. Konvalinka, and F. A. Matsen IV, On the enumeration of tanglegrams and tangled chains, arXiv:1507.04976 [math.CO], 2015.
• Ira M. Gessel, Counting tanglegrams with species, arXiv:1509.03867 [math.CO], (13-September-2015)
• F. A. Matsen IV, S. C. Billey, D. A. Kas, and M. Konvalinka, Tanglegrams: a reduction tool for mathematical phylogenetics, arXiv:1507.04784 [q-bio.PE], 2015.
• Frederick A. Matsen, Sage/GAP4 Code for generating tanglegrams

Crossrefs

Cf. A258620 (tanglegrams), A259114, A259116, A258486 (tangled chains), A258487, A258488, A258489.

Programs

PARI

\\ See links in A339645 for combinatorial species functions.
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)}
cycleIndexSeries(n)={my(g=rootedBinTrees(n), u = g + (sRaise(g,3) - g^3)/3); sCartProd(u,u)}
NumUnlabeledObjsSeq(cycleIndexSeries(12)) \\ Andrew Howroyd, Dec 24 2020

Extensions

More terms from Ira M. Gessel, Jul 19 2015

Terms a(15) and beyond from Andrew Howroyd, Dec 24 2020