What does this recursive snippet of Java code do?

Question

I passed through this recursion example, but I couldn't find out its purpose. Could you please help me?

public static int somerec(int n, int x, int y) {
    if (n < x*y)
        return 0;
    else if (n == x*y)
        return 1;
    else {
        int sum = 0;
        for (int i = x; i <= n;i++)
             sum += somerec(n-i, i, y-1);
        return sum;
    }
}

This is not a homework.

Answer 1

Perhaps running the code may help you understand?

Here's my quick-n-dirty reimplementation in Python:

def somerec(n, x, y):
    if n < x*y:
        return 0
    if n == x*y:
        return 1
    sum_ = 0
    for i in range(x, n+1):
        sum_ += somerec(n-i, i, y-1)
    return sum_

Trying it out:

>>> [somerec(i, 1, 2) for i in range(30)]
[0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 
12, 13, 13, 14, 14]
>>> [somerec(i, 1, 3) for i in range(30)]
[0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 37, 40,
44, 48, 52, 56, 61, 65, 70]
>>> [somerec(i, 1, 4) for i in range(30)]
[0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 23, 27, 34, 39, 47, 54, 64, 72, 84, 
94, 108, 120, 136, 150, 169, 185]
>>> [somerec(i, 2, 4) for i in range(30)]
[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 23, 27, 34, 39, 47, 54,
64, 72, 84, 94, 108, 120]

Answer 2

It sorts out those students with good analytical capabilities from those without.

As such, it's a valuable tool for educators to figure out which students should be given a passing grade and which ones should be nudged towards a career in a different area :-)

Answer 3

Well this may sound ridiculous but that function:

Returns the number for times the product of x times y is exactly n

What I can't tell are the increments of n,x and y nor what do they describe.

For instance

for f( n=8, x=2, y=3) the value is 2 ( when

n=0, x=4, y=0,

n=3, x=3, y=1 )

f( n=9, x=2, y=3) the value is 3 ( when

n=0, x=5, y=0 ,

n=0, x=4, y=0,

n=6, x=3, y=2 )

Each time the product of x times y is exactly n the count increments.

I cross post this to mathoverflow to see if someone there knows the answer.