  N-site-lattice Hamiltonians H are introduced and perceived as a set of
systematic discrete approximants of a certain PT-symmetric
square-well-potential model with the real spectrum and with a non-Hermiticity
which is localized near the boundaries of the interval. Its strength is
controlled by one, two or three parameters. The problem of the explicit
construction of a nontrivial metric which makes the theory unitary is then
addressed. It is proposed and demonstrated that due to the not too complicated
tridiagonal-matrix form of our input Hamiltonians the computation of the metric
is straightforward and that its matrix elements prove obtainable,
non-numerically, in elementary polynomial forms.
