  Exact sequences of Feigin-Stoyanovsky's type subspaces for affine Lie algebra
$\mathfrak{sl}(l+1,\mathbb{C})^{\widetilde{}}$ lead to systems of recurrence
relations for formal characters of those subspaces. By solving the
corresponding system for $\mathfrak{sl}(3,\mathbb{C})^{\widetilde{}}$, we
obtain a new family of character formulas for all Feigin-Stoyanovsky's type
subspaces at general level.
