Maximal subgroup growth of a few polycyclic groups

We give here the exact maximal subgroup growth of two classes of polycyclic groups. Let $G_k = \langle x_1, x_2, …, x_k \mid x_ix_jx_i^{-1}x_j \text{ for all } i < j \rangle$\mathrm{.}So$G_k = $\mathbb{Z}$ \rtimes ($\mathbb{Z}$ \rtimes ($\mathbb{Z}$ \rtimes … \rtimes $\mathbb{Z}$)$\mathrm{.}Thenforall$k \geq 2$, we calculate $m_n(G_k)$, the number of maximal subgroups of $G_k$ of index $n$, exactly. Also, for infinitely many groups $H_k$ of the form $$\mathbb{Z}$^2 \rtimes G_2$,wecalculate$m_n(H_k)$ exactly.