On the Diophantine equation n2=x2+by2+cz2

For any positive integer n we state and prove formulas for the number of solutions, in integers, of n2=x2+y2+2z2, n2=x2+2y2+2z2, n2=x2+y2+3z2 and n2=x2+3y2+3z2. Some conjectures are listed at the end of the paper.