Question

Consider the equation x_1 + x_2 + x_3 + x_4 = n where X_i >= 0 integers. x_2 >=2 x_3 is multiple of four and 1<=x_4<=3. Let Cn be number of solutions to this equation subject to these restrictions. find generating function for the sequecne {c_n : n>=0} and use it to find closed formula for c_n

Answer 1

so i have xx_1= 1/1-x
x_2 =x^2/1-x
x_3=1/(1-x^4)
x_4= x+x^2+X^3

but i am not sure what to do with this now