This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359797 #19 Jul 30 2023 19:10:13 %S A359797 1,3,15,87,547,3623,24885,175591,1265187,9271167,68894785,518053231, %T A359797 3935274277,30158804835,232930956175,1811476156847,14174669041427, %U A359797 111532445963367,882004732285473,7006931317108119,55899039962599777,447666261592033123 %N A359797 Cogrowth sequence of the lamplighter group Z_2 wr Z where wr denotes the wreath product. %C A359797 a(n) is the number of words of length 2n in the letters a,t,t^(-1) that equal the identity of the lamplighter group Z_2 wr Z = <a,t | a^2=1, [a,t^(-k)at^k]=1 for all k >. %C A359797 Walks on this group can be seen as operations on an infinite tape of 0's and 1's where each step is either a right shift, left shift or toggles the current element. a(n) is then the number of sequences of 2n such moves which return the tape to the initial position. %H A359797 Andrew Elvey Price, <a href="/A359797/b359797.txt">Table of n, a(n) for n = 0..500</a> %H A359797 Andrew Elvey Price and A. J. Guttmann, <a href="https://arxiv.org/abs/1706.07571">Numerical studies of Thompson's group F and related groups</a>, arXiv:1706.07571 [math.GR], 2017. %H A359797 D. Revelle, <a href="https://doi.org/10.1214/ECP.v8-1092">Heat kernel asymptotics on the lamplighter group</a>, Electronic Communications in Probability 8 (2003), 142-154. %H A359797 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lamplighter_group">Lamplighter group</a> %Y A359797 Spherical growth sequence for this group is A288348. %Y A359797 Cf. A359798. %K A359797 nonn,walk %O A359797 0,2 %A A359797 _Andrew Elvey Price_, Jan 13 2023