  We establish lower bounds for the entropy of the Hard Core Model on a few 2d
lattices $\scriptstyle {\rm {\bf L}}.$ In this model the allowed configurations
inside $\scriptstyle \{0,1\}^{{\rm {\bf L}}}$ are the one's in which the
nearest neighbor $\scriptstyle 1$'s are forbidden. Our method which is based on
a sequential fill-in scheme is unbiassed and thereby yields in principle
arbitrarily good estimates for the topological entropy. The procedure also
gives some detailed information on the support of the measure of maximal
entropy.
