Determine the number of integer solutions to:
|x|+ |y| + |z| = 15

Note:

The absolute value function F(x) = |x| is defined as:

        x if x ≥ 0
F(x) = 
       -x if x < 0

(In reply to General Solution -- Two geometric methods by Steve Herman)

Perhaps someone can do the algebra to prove

C(n-1,2)*8 + (C(n+2,2)-C(n-1,2)-3)*4 + 6 = 4*n^2 + 2

the LHS of which is the generalization of my method.

Posted by Charlie on 2014-02-20 09:56:14