Write a grammar for language $a^ib^jc^k$

Question

Problem:

Write a grammar for a language: $$L=\{ a^ib^jc^k : j=2(i+k)+1 \}$$

My solution:

$S \rightarrow AbB$

$A \rightarrow \epsilon$

$A \rightarrow aAbb$

$B \rightarrow \epsilon$

$B \rightarrow bbBc$

I am not sure if it is correct, so I would be grateful if someone checked it. Thanks in advance!