MathDemos:Triangle of m=2ij+i+j

For all the ${\displaystyle \scriptstyle m\,=\,2ij+(i+j),\,1\,\leq \,\,j\,\leq \,i,\,}$ entries of the following table, corresponds an odd composite number ${\displaystyle \scriptstyle N=2m+1=(2i+1)(2j+1)=2(2ij+i+j)+1,m\,\geq \,4\,}$. All composite odd numbers ${\displaystyle \scriptstyle N\,=\,2m+1,\,m\,\geq \,4,\,}$ have one or more entries ${\displaystyle \scriptstyle m\,=\,2ij+(i+j),\,1\,\leq \,\,j\,\leq \,i,\,}$ in the table.

The j-th colum is is an arithmetic progression with a common difference of $d=2j+1$.

GridGraph[{i+1,j+1}] has $2ij+i+j$ edges in total, increasing $2i+2j$ edges from GridGraph[{i,j}]