We adopt the Hartree-Fock (HF) method in the proton-neutron-Λ (p-n-Λ) formalism and the nucleon-Λ Tamm-Dancoff Approximation (NΛ TDA) to study the energy spectra of medium-mass hypernuclei. The formalism is developed for a potential derived from effective field theories which includes explicitly the 3-body N N N forces plus the Y N LO potential. The energy spectra of selected medium-mass hypernuclei are presented and their properties discussed. The present calculation is the first step of a project devoted to ab initio studies of hypernuclei in medium and heavy mass regions. This may provide a guide for a better understanding of the Y N interactions at momentum scales not accessible in few-body hypernuclei.