login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258487 Number of tangled chains of length k=4. 8
1, 1, 14, 2140, 1017219, 1110178602, 2320017306125, 8278981347401059, 46556715158334549170, 388779284837787599307987, 4605471565794120802036550000, 74633554055057890778698344509705, 1606481673354648219373898238155693682, 44821655543075499856527523557216582931002 (list; graph; refs; listen; history; text; internal format)
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, MatjaĆŸ 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 27 09:53 EDT 2021. Contains 348273 sequences. (Running on oeis4.)