Is there a closed form for $y=\sum_{k=0}^{n} x^{a^k}$ Where $a$ is constant?

$y=x+x^{a}+x^{a^2}+x^{a^3}+...+x^{a^n}$

Note that $k$ is a power to $a$ not $x$.

It is simple to find a closed form for $\sum_{k=0}^{n} x^{k}$

which is $\frac {1-x^n}{1-x}$

but I tried to find a closed form for $\sum_{k=0}^{n} x^{a^k}$ without any useful results.