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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
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
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.
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Ira M. Gessel, Jul 19 2015
Terms a(15) and beyond from Andrew Howroyd, Dec 24 2020
STATUS
approved