Folner sequence of $\mathbb{Z}[\frac{1}{2}]$

Question

Consider $\mathbb{Z}[\frac{1}{2}]$ consisting of rational numbers of the form $k2^l$ with $k,l\in\mathbb{Z}$. Under addition and discrete topology $\mathbb{Z}[\frac{1}{2}]$ is a discrete abelian group, hence a countable discrete amenable group.

Question: Can we write down explicitly a Folner sequence of $\mathbb{Z}[\frac{1}{2}]$?