A258489 Number of tangled chains of length k=6.

1, 1, 122, 474883, 11168414844, 989169269347359, 250335000079534559375, 151038989624520433840089358, 191158216491241179675824199407135, 461408865973380293005829125668717407727, 1973397409908124305318632313047269426852165625, 14104214451439837037643144221899175649593123932192274

Offset

1,3

Comments

Tangled chains are ordered lists of k rooted binary trees with n leaves and a matching between each leaf from the i-th tree with a unique leaf from the (i+1)-st tree up to isomorphism on the binary trees. This sequence fixes k=6, and n = 1,2,3,...

References

R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.

Links

Table of n, a(n) for n=1..12.

Sara Billey, Matjaž Konvalinka, and Frederick A. Matsen IV, On the enumeration of tanglegrams and tangled chains, arXiv:1507.04976 [math.CO], 2015.

Formula

t(n) = Sum_{b=(b(1),...,b(t))} Product_{i=2..t} (2(b(i)+...+b(t))-1)^6)/z(b) where the sum is over all binary partitions of n and z(b) is the size of the stabilizer of a permutation of cycle type b under conjugation.

Crossrefs

Cf. A000123 (binary partitions), A258620 (tanglegrams), A258485, A258486, A258487, A258488, A258489 (tangled chains), A259114 (unordered tanglegrams).

Sequence in context: A098129 A198603 A237640 * A015079 A015042 A062233

Adjacent sequences: A258486 A258487 A258488 * A258490 A258491 A258492

Keyword

nonn

Author

Sara Billey, Matjaz Konvalinka, and Frederick A. Matsen IV, May 31 2015

Status

approved