A258488 Number of tangled chains of length k=5.

1, 1, 41, 31732, 106420469, 1046976648840, 24085106680575625, 1117767454807330938472, 94308987414050519542935029, 13390317159105772877158700776107, 3014130596940522685213135526859317500, 1025828273466214412416440210115479183065903, 507888918625036626314714587415852381698509422634

Offset: 1

Author

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

Keywords

• nonn

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

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

Crossrefs

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

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.