  We calculate the reduced density matrix of a block of integer spin-S's in a
q-deformed valence-bond-solid (VBS) state. This matrix is diagonalized exactly
for an infinitely long block in an infinitely long chain. We construct an
effective Hamiltonian with the same spectrum as the logarithm of the density
matrix. We also derive analytic expressions for the von Neumann and R\'enyi
entanglement entropies. For blocks of finite length, we calculate the
eigenvalues of the reduced density matrix by perturbation theory and numerical
diagonalization. These results enable us to describe the effects of finite-size
corrections on the entanglement spectrum and entropy in this generalized VBS
model.
