  The trigonometric six-vertex model with domain wall boundary conditions and
one partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, is
considered. The partition function is computed using the Izergin-Korepin
method, generalizing the result of Foda and Zarembo from the rational to the
trigonometric case. Thereafter we specify the parameters in Kuperberg's way to
get a formula for the number of states as a determinant of Wilson polynomials.
We relate this to a type of ASM-like matrices.
