We study antiferromagnetic, S=1/2 Heisenberg models with nearest- and secon
d-neighbor interactions on the one-fifth depleted square lattice which desc
ribes the spin degrees of freedom in the spin-gap system CaV4O9. The metapl
aquette expansion for the triplet excitation spectrum is extended to fifth
order, and the results are compared with experimental data on CaV4O9. We at
tempt to locate the phase boundary between magnetically ordered and gapped
phases. [S0163-1829(98)02146-8].