  A three-fermion problem in a three-dimensional lattice with anisotropic
hopping is solved by discretizing the Schroedinger equation in momentum space.
Interparticle interaction comprises on-site Hubbard repulsion and in-plane
nearest-neighbor attraction. By comparing the energy of three-fermion bound
clusters (trions) with the energy of one pair plus one free particle, a trion
formation threshold is accurately determined, and the region of pair stability
is mapped out. It is found that the "close-packed" density of fermion pairs is
highest in a strongly anisotropic model. It is also argued that pair
superconductivity with the highest critical temperature is always close to
trion formation, which makes the system prone to phase separation and local
charge ordering.
