Hello, I am having difficulty trying to understand and solve this combinatorics question. I know that the number of non-negative integer solutions to

?????1 + ?????2 + ?????3 + ?????4 = n is ??(?4?1?n+4?1??)?? , for this question I know I should subtract accordingly, say ?????1 + ?????2 + ?????3 + ?????4 = n - 10 with ?????1 ????? 0. But now how should I proceed with this question? How would an expert solve this question? Thank you so much!

Question 7. [10 marks] For a nonnegative integer n, let an be the number of non-negative integer solutions to the equation 1131 +2$2+$3+2$4 =17}, with $1 2 10 and 1 S :34 g 10. Find the ordinary generating function of an