How many squares can be filled in the NxN grid such that no 5 orthogonal neighbors are all filled?

no_orthogonal.py

from ortools.sat.python import cp_model
import sys

# How many squares can be filled in the 10x10 grid such that no five
# orthogonally-connected squares are all filled?

m = cp_model.CpModel()

size = 10

if len( sys.argv ) == 2:
    size = int( sys.argv[1] )

vars = [ [ m.NewIntVar( 0, 1, f"g_{i}_{j}" ) for j in range( size ) ]
         for i in range( size ) ]

for i in range( 1, size - 1 ):
    for j in range( 1, size - 1 ):
        m.Add( vars[i][j] + vars[i-1][j] + vars[i][j-1] + vars[i+1][j] + vars[i][j+1] < 5)
        
m.Maximize( sum( vars[i][j] for i in range( size ) for j in range( size ) ) )

solver = cp_model.CpSolver()
status = solver.Solve( m )

def show_soln():
    for i in range( size ):
        print( "".join( str( solver.Value( vars[i][j] ) )
                        for j in range( size )))

    print()
    print( sum( solver.Value( vars[i][j] ) for i in range(size) for j in range( size) ) )
    
if status == cp_model.OPTIMAL:
    print( "OPTIMAL" )
    show_soln()
elif status == cp_model.FEASIBLE:
    print( "FEASIBLE" )
    show_soln()
else:    
    print( "No solution found." )