  In the framework of an inhomogeneous solvable lattice model, we derive exact
expressions for a boundary-to-boundary current on a lattice of finite width.
The model we use is the dilute $O(n=1)$ loop model, related to the
Izergin-Korepin spin-1 chain and the critical site percolation on the
triangular lattice. Our expressions are derived based on solutions of the
$q$-Knizhnik-Zamolodchikov equations, and recursion relations.
