The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #26 Jul 30 2023 18:22:36
%S 1,4,28,232,2108,20384,206392,2165720,23385340,258532216,2915343808,
%T 33437862352,389230520888,4590271681064,54767161155000,
%U 660307913374352,8036973478493436,98672644594401736,1221090110502080440,15222093531642444504
%N Cogrowth sequence of the group Z wr Z where wr denotes the wreath product.
%C 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 >.
%H Andrew Elvey Price, <a href="/A359798/b359798.txt">Table of n, a(n) for n = 0..500</a>
%H Andrew Elvey Price and A. J. Guttmann, <a href="http://arxiv.org/abs/1706.07571">Numerical studies of Thompson's group F and related groups</a>, arXiv:1706.07571 [math.GR], 2017.
%H C. Pittet and L. Saloff-Coste, <a href="https://doi.org/10.1214/aop/1023481013">On random walks on wreath products</a>, The annals of probability, 30 No. 2 (2002), 948-977.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wreath_product">Wreath product</a>
%Y Related cogrowth sequences: A359797, A359705. Spherical growth sequence for this group is A294782.
%K nonn
%O 0,2
%A _Andrew Elvey Price_, Jan 13 2023