numbers

S = N(N^2 + 1)/(2), or rather N^2(N^2+1)/2, or even (N^4 + N^2)/2, or most importantly: [m(m+1)/2]/N, where arithmetically 1+2+3+...+m, where m = N^2 for N^2 base units per square, and where S= the "magic sum" of the N horizontal rows and N vertical columns of base units, as well as the sums of the main diaganols. Here are examples of the first, or smallest, seven number squares used to differentiate the seven different sized squares: