Sum count algorithm name

Question

I want to find out what this algorithm is called

int s(int m, int n) {
    if (m == 1 || n == 1) {
        return 1;
    } else if (n >= m) {
        return s(m, m - 1) + 1;
    } else {
        return s(m - n, n) + s(m, n - 1);
    }
}

I think it counts possible sums with limited summands

like s(5,5)=7

1. 1+1+1+1+1
2. 2+1+1+1
3. 2+2+1
4. 3+1+1
5. 3+2
6. 4+1
7. 5

Answer 1

Found a solution:

for (int y = 1; y <= m; y++) {
    for (int x = 1; x <= m; x++) {

        if (x == 1 || y == 1) {
            arr[y][x] = 1
        } else if (x == y) {

            arr[y][x] = arr[y - 1][x] + 1

        } else if (y > x) {
            arr[y][x] = arr[y - 1][x]

        } else if (x > 1 && y > 1) {

            arr[y][x] = arr[y - 1][x] + arr[y][x - y]
        }   

    }

}