The middle row of the principal cell

The zeros of the array D¯p(i,j) obtained from the Delannoy numbers D(i,j)D(i,j) modulo an odd prime p   give an interesting pattern. Since the numbers D(i,j)D(i,j) satisfy the Lucas property only the zeros of the so-called principal cell are relevant. The standard combinatorial expression for D(i,j)D(i,j) in the language of lattice paths will be derived and the entries on the middle row of the principal cell will be discussed.