A numerical quantum transfer-matrix approach for the S = 1 macroscopic chains with the single-site anisotropy and alternating bonds is worked out and a fit of the susceptibility data for the quasi-one-dimensional molecular magnets [Ni(dmen)(mu - N-3)(2)](n) and [Ni(aep)(mu - N-3)(2)](n) is performed in the region above the observed low-temperature minima.