A258486 Number of tangled chains of length k=3.

1, 1, 5, 151, 9944, 1196991, 226435150, 61992679960, 23198439767669, 11380100883484302, 7087878538028540725, 5465174495550911165171, 5111311778783673593594175, 5701234859347275019419890715, 7477492710871626347942014991975, 11393306956061559325223329489826611, 19958666934810234750929365717573438949, 39835206091758734935374720734513530255512, 89867076346063005007676287874769844881101800, 227547795689116560408812799327387232156371842150

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=3, 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..20.

Sara Billey, Matjaž Konvalinka, and Frederick A. Matsen IV, On the enumeration of tanglegrams and tangled chains, (2015).

Formula

t(n) = Sum_{b=(b(1),...,b(t))} Product_{i=2..t} (2(b(i)+...+b(t))-1)^3)/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), A258485 (tanglegrams), A258487, A258488, A258489.

Sequence in context: A041431 A107691 A181979 * A082623 A332115 A262655

Adjacent sequences: A258483 A258484 A258485 * A258487 A258488 A258489

Keyword

nonn

Author

Sara Billey, May 31 2015

Status

approved