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

1,4

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

Prog

(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

Crossrefs

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

Keyword

nonn

Author

Frederick A. Matsen IV, Jun 18 2015

Extensions

More terms from Ira M. Gessel, Jul 19 2015

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

Status

approved