In the paper Hernandez and Leclerc - Cluster algebras and quantum affine algebras, Section 13.5, it is said that when $\mathfrak{g}$ is of type $A_2$ and $\ell=2$, then the corresponding cluster algebra $\mathscr{A}_2$ for $U_q(\widehat{\mathfrak{g}})$ is of finite cluster type $D_4$. There are 16 cluster variables.

It is said that (1) when $\mathfrak{g}$ is of type $A_2$ and $\ell=3$, (2) when $\mathfrak{g}$ is of type $A_2$ and $\ell=4$, (3) when $\mathfrak{g}$ is of type $A_3$ and $\ell=2$, and (4) when $\mathfrak{g}$ is of type $A_4$ and $\ell=2$, the corresponding cluster algebras are also finite type cluster algebras. How many cluster variables do we have in the cases (1), (2), (3), and (4)? Thank you very much.