## Dr Roy H Ogawa

Let *Z* = integers,

For any integer k > 0, *Z ^{k}* is the k dimensional product space consisting of z = (z

_{1}, . . . z

_{k})

where the z

_{i}are in Z.

For any integer r ≥ 0,

*D(k,r)*= { z in Z

^{k}: for each i, z

_{i}≥ 0, & Σ

_{i=1}

^{k}z

_{i}= r }