A259116 Number of unrooted binary unordered tanglegrams of size n.

1, 1, 1, 2, 4, 22, 145, 1875, 31929, 698183, 18056523, 538340256, 18141423039, 681939320185

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 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), A259114, A259115, A258486 (tangled chains), A258487, A258488, A258489.

Sequence in context: A321248 A309741 A110130 * A283322 A019025 A264729

Adjacent sequences: A259113 A259114 A259115 * A259117 A259118 A259119

Keyword

nonn,more

Author

Frederick A. Matsen IV, Jun 18 2015

Extensions

More terms from Ira M. Gessel, Jul 19 2015

Status

approved