# Unrestricted grammar to generate $a^{n^2}$

I have been asked to find a grammar that will generate the language $\{a^{n^2}:n \ge0\}$ in an exercise. So far I tried to replicate the previously written characters with my grammar rules but it didn't work. Any idea on how to setup such grammar? Any help will be appreciated.

Found the answer here. Basically the grammar looks like this: $$S→LAYR \\ ZA→aAZ \\ Za→aZ \\ ZR→AAYR \\ aY→Ya \\ AY→YA \\ LY→LZ \\ YR→X \\ aX→Xa \\ AX→Xa \\ LX→ε \\$$
Set aside $n$ of the $n^2$ characters, and use that $(n+1)^2 = n^2 + 2n +1$.
So at any moment we have (say) $n^2-n$ symbols $A$ and $n$ symbols $B$. We also need endmarkers. $L,R$ count as A$.$S\to LBBR$In one linear phase we visit all symbols, and each symbol$B$will generate two extra$A$'s. Finally we add a$B$.$L \to LX$;$XA\to AX$;$XB\to AABX$;$XR\to BR$Nondeterministically end, transforming all symbols into$a\$.