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Exercise U

Posted 10/04/2015
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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)`.