  We treat three-dimensional bosonic clusters wih up to N=40 atoms, interacting
additively through two-body Van der Waals potentials, in the near-threshold
regime. Our study inludes super-borromean systems with N atoms for which all
subsystems are unbound. We determine the energetics and structural properties
as the expectation value of the interparticle distance as a function of the
coupling strength. It has been shown that the coupling strength g*(N), for
which the N-body systems becomes unbound, is bounded by the coupling constant
g*(N-1) for which the next smaller system with N-1 atoms becomes unbound, i.e.,
g*(N) >= (N-1)/Ng*(N-1). By fitting our numerically determined ground state
energies to a simple functional form with three fitting parameters, we
determine the relationship between g*(N) and g*(N-1). Our trimer and tetramer
energies fall on the so-called Tjon line, which has been studied in nuclear
physics. We confirm the existence of generalized Tjon lines for larger
clusters. Signatures of the universal behavior of weakly-bound
three-dimensional clusters can possibly be observed in ultracold Bose gases.
