A258485 Number of tangled chains of length k=7.

1, 1, 365, 7119961, 1172597933594, 934741501255380321, 2602204282373953017437500, 20410544568790568555722851029455, 387481340785957748099474582410763014214, 15899856312608503503306403988460714538830399657

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..10.

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)^7)/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: A208321 A208391 A208398 * A073305 A248552 A259077

Adjacent sequences: A258482 A258483 A258484 * A258486 A258487 A258488

Keyword

nonn

Author

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

Status

approved