  Starting from the T-Q equations of the open spin-1 XXZ quantum spin chain
with general integrable boundary terms, for values of the boundary parameters
which satisfy a certain constraint, we derive a set of nonlinear integral
equations (NLIEs) for the inhomogeneous open spin-1 XXZ chain. By taking the
continuum limit of these NLIEs, and working in analogy with the open spin-1 XXZ
chain with diagonal boundary terms, we compute the boundary and the Casimir
energies of the corresponding supersymmetric sine-Gordon (SSG) model. We also
present an analytical result for the effective central charge in the
ultraviolet (UV) limit.
