A359798 Cogrowth sequence of the group Z wr Z where wr denotes the wreath product.

1, 4, 28, 232, 2108, 20384, 206392, 2165720, 23385340, 258532216, 2915343808, 33437862352, 389230520888, 4590271681064, 54767161155000, 660307913374352, 8036973478493436, 98672644594401736, 1221090110502080440, 15222093531642444504

Offset

0,2

Comments

a(n) is the number of words of length 2n in the letters a,a^(-1),t,t^(-1) that equal the identity of the group Z wr Z = <a,t | [a,t^(-k)at^k]=1 for all k >.

Links

Andrew Elvey Price, Table of n, a(n) for n = 0..500

Andrew Elvey Price and A. J. Guttmann, Numerical studies of Thompson's group F and related groups, arXiv:1706.07571 [math.GR], 2017.

C. Pittet and L. Saloff-Coste, On random walks on wreath products, The annals of probability, 30 No. 2 (2002), 948-977.

Wikipedia, Wreath product

Crossrefs

Related cogrowth sequences: A359797, A359705. Spherical growth sequence for this group is A294782.

Sequence in context: A229647 A229646 A229645 * A307468 A202824 A046904

Adjacent sequences: A359795 A359796 A359797 * A359799 A359800 A359801

Keyword

nonn

Author

Andrew Elvey Price, Jan 13 2023

Status

approved