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

Author

Andrew Elvey Price, Jan 13 2023

Keywords

• nonn

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 = .

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.