Context-free grammar for language involving multiplication I'm struggling to find the context-free grammar for the following language:
$$
L = \{a^sb^tc^m:s,t,m\in\mathbb{N}^+\land1\leq t\leq3\land s\times t=m\}
$$
Any help would be appreciated.
Write $L$ in the following way:
$$
L = \{ a^sbc^s : s \in \mathbb{N}^+ \} \cup \{ a^sb^2c^{2s} : s \in \mathbb{N}^+ \} \cup \{ a^sb^3c^{3s} : s \in \mathbb{N}^+ \}.
$$