[en] A model operator H_μ, μ > 0 associated to a system of three particles on the three-dimensional lattice Z³. We study the case where the parameter function w has a special form with the nondegenerate minimum at the n, n > 1 points. If the associated Friedrichs model has a zero energy resonance, then we prove that the operator H_μ has infinitely many negative eigenvalues accumulating at zero. Moreover, we obtain an asymptotic value for the number of negative eigenvalues of H_μ lying below z < 0 with respect to the spectral parameter z → -0. (author)