Suppose Q is a positive nonsquare integer congruent to 0 or 1 mod 4. Then for every positive integer n, there exists a unique pair (j,k)$ of positive integers such that (j+k+1)²-4k = Qn² . This representation is used to generate the fixed-j array for Q and the fixed-k array for Q. These arrays are proved to be dispersions; i.e., each array contains every positive integer exactly once and has certain compositional and row-interspersion properties.