  In this note, we consider the six-vertex model with domain wall boundary
conditions, defined on a $M\times M$ lattice, in the inhomogeneous case where
the partition function depends on 2M inhomogeneities $\lambda_j$ and $\mu_k$.
For a particular choice of the set of $\lambda_j$ we find a new determinant
representation for the partition function, which allows evaluation of the bulk
free energy in the thermodynamic limit. This provides a new connection between
two types of determinant formulae. We also show in a special case that spin
correlations on the horizontal line going through the center coincide with the
ones for periodic boundary conditions.
