This exercise is about number of solutions for Diophantine equations.
Suppose `x_1,x_2,x_3,x_4,n` are nonnegative integers such that
`x_1+2x_2+3x_3+4x_4=n` and `0\le x_1 \le 2`.
`a(n)` is the number of solutions `(x_1,x_2,x_3,x_4)` for the above constraint linear Diophantine equation.
For example, `a(3)=2` because we have `2` solutions: `(0,0,1,0)`, `(1,1,0,0)`.
Find `a(n)`.