I am interested in a grammar for the language L which defined as follows: $$ L=\left\{ { a }^{ n }{ b }^{ n/2 }{ c }^{ n }\mid n\bmod2=0,\quad n\in\mathbb N \right\} $$ My idea is to substitute n with 2m because only even integers are accepted, which are completely divisible by 2. So that I would come to the following: $$ L=\left\{ { a }^{ 2m }{ b }^{ m }{ c }^{ 2m }\mid m\in \mathbb N \right\} $$ The grammar generates words, such as aabcc, aaaabbcccc.
My attempts to construct a clever grammar for the language L have not been successful so far. I am very curious if anyone can help me.