Verhagen’s conditions for Markovian behavior in the 2-d plane-square Ising lattice gas model with both nearest and next nearest neighbor interactions are cast in the form of a single nonlinear equation that is solved numerically. If ε1 and ε2 are the nearest and next nearest neighbor interaction energies, respectively, then there are no solutions for both ε1 and ε2 negative (representing attractive interactions). For ε2≳0, there is a locus in the ε1-density plane for both ε1≳0 and ε1<0 where the model is Markovian and where one can calculate the activity exactly as a function of density and the interaction parameters; the special point ε1=+∞ corresponds to the analytic solution found by Verhagen.