How to find the number of combinations?

Question

Combinatorics

For example, there is a number n (let it be 7) and a number a (4), we need to find the number of combinations when adding a (4) numbers we get the number n (7).
Well, it can still be solved by enumeration, and if we have large numbers such as n (2500) and a (500).

Answer 1

Infinite amount.
1+1+1+4 = 7
1+1+2+3 = 7
1+1+3+2 = 7
1+1+4+1 = 7
1+1+5+0 = 7
1+1+6 +(-1) = 7
...