  The critical behavior of the 1/5-depleted square-lattice Ising model with
nearest neighbor ferromagnetic interaction has been investigated by means of
both an exact solution and a high-temperature series expansion study of the
zero-field susceptibility. For the exact solution we employ a decoration
transformation followed by a mapping to a staggered 8-vertex model. This yields
a quartic equation for the critical coupling giving $K_{c} (\equiv\beta J_{c})
=0.695$. The series expansion for the susceptibility, to $\mathcal{O}(K^{18})$,
when analyzed via standard Pad\'{e} approximant methods gives an estimate of
K$_{c}$, consistent with the exact solution result to at least four significant
figures. The series expansion is also analyzed for the leading amplitude and
subdominant terms.
