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A259115 Number of unrooted binary ordered tanglegrams of size n. 3
1, 1, 1, 2, 4, 31, 243, 3532, 62810, 1390718, 36080361, 1076477512, 36281518847, 1363869480379, 56587508558171, 2569141702825037, 126714642738385906, 6747643861563535720, 385875940575529343271, 23588199955061659841248, 1535037278334227258123709, 105961521687913311720698169 (list; graph; refs; listen; history; text; internal format)



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.


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


(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


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

Sequence in context: A220283 A339603 A188113 * A051569 A087186 A051759

Adjacent sequences:  A259112 A259113 A259114 * A259116 A259117 A259118




Frederick A. Matsen IV, Jun 18 2015


More terms from Ira M. Gessel, Jul 19 2015

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



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Last modified May 24 18:27 EDT 2022. Contains 354043 sequences. (Running on oeis4.)