A258487 Number of tangled chains of length k=4.

1, 1, 14, 2140, 1017219, 1110178602, 2320017306125, 8278981347401059, 46556715158334549170, 388779284837787599307987, 4605471565794120802036550000, 74633554055057890778698344509705, 1606481673354648219373898238155693682, 44821655543075499856527523557216582931002

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=4, and n = 1,2,3,...

References

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

Links

S. Billey, Table of n, a(n) for n = 1..20

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)^4)/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: A198601 A233076 A134814 * A206753 A279577 A015515

Adjacent sequences: A258484 A258485 A258486 * A258488 A258489 A258490

Keyword

nonn

Author

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

Status

approved