Number of integral solutions for $|x | + | y | + | z | = 10$ How can I  find the number of integral solution to the
equation
$|x | + | y | + | z | = 10.$
I am using the formula,
Number of integral solutions for $|x| +|y| +|z| = p$ is $(4P^2) +2 $, So the answer is 402.
But, I want to know, How we can find it without using formula.
any suggestion !!!
Please help

I think it must 8 times the number of intergral solution to equation:
$$x+y+z=10$$
So the result is :
$$8C_{12}^2=528$$
