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A258488 Number of tangled chains of length k=5. 8
1, 1, 41, 31732, 106420469, 1046976648840, 24085106680575625, 1117767454807330938472, 94308987414050519542935029, 13390317159105772877158700776107, 3014130596940522685213135526859317500, 1025828273466214412416440210115479183065903, 507888918625036626314714587415852381698509422634 (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=5, 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..13.

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)^5)/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: A214338 A084275 A218377 * A297052 A238566 A241327

Adjacent sequences:  A258485 A258486 A258487 * A258489 A258490 A258491

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 31 08:46 EDT 2020. Contains 338101 sequences. (Running on oeis4.)