jmc

Notice that all odd numbers can be obtained by using $(a+1{)}^2-a^2=2a+1,$ where $a$ is a nonnegative integer. All multiples of $4$ can be obtained by using $(b+1{)}^2-(b-1{)}^2=4b$, where $b$ is a positive integer. Numbers congruent to $2(\mathrm{mod}4)$ cannot be obtained because squares are $0,1(\mathrm{mod}4).$ Thus, the answer is $500+250=\boxed{750}.$