A259114 Number of rooted binary unordered tanglegrams of size n.

1, 1, 2, 10, 69, 807, 13048, 269221, 6660455, 191411477, 6257905519, 229312906604, 9309547057292, 414803750101863

Offset

1,3

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. Rooted means that the tanglegram is composed of rooted trees, and unordered means that two tanglegrams that differ by exchanging the trees and inverting the bijection are considered identical.

Links

Table of n, a(n) for n=1..14.

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), A259115, A259116, A258486 (tangled chains), A258487, A258488, A258489.

Sequence in context: A325054 A139715 A293914 * A051575 A121201 A166076

Adjacent sequences: A259111 A259112 A259113 * A259115 A259116 A259117

Keyword

nonn,more

Author

Frederick A. Matsen IV, Jun 18 2015

Extensions

More terms from Ira M. Gessel, Jul 19 2015

Status

approved