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

re: General Solution -- Two geometric methods by Charlie)

Well, Charlie, since you put it that way, this matches up to my second method.

C(n-1,2)*8 = number of integral points on side of the octahedron excluding edges = 4n^2 - 12n + 8

(C(n+2,2)-C(n-1,2)-3)*4 = number of integral points on edges of the octahedron excluding vertices = 12n - 12

6 = number of vertices on octahedron

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