The expression that results from raising the pattern function of a symmetric linear array of equispaced point sources to some integer power greater than unity can be identified as the pattern function of a larger symmetric linear array of point sources with the same spacing. In this manner, one may determine a distribution of source strengths for a large array so that its pattern displays characteristic features of a smaller array, such as fewer sidelobes. In the case where the original pattern function is raised to an even power, the sidelobes of the pattern of the associated larger array all have the same phase.