Problem with a recusive partition(number theory) function

Question

Example: Let’s say your user input is 6.
Then the number of sequences that sum up to 6 is 11 (including 6 itself). :

The problem i am having is that it works when the user enters 1 or 6 but else it is way off and i cant figure out why.

Partition can give more info on the subject if needed.

Thanks in advance.

#include <iostream>

using namespace std;

int sum(double number, int min, int & counter)
{
    int temp=0, n;
    n=number+temp;

    if (number>=(n/2.0)+.5 && (number!=1))
    {
        number --;
        temp ++;
        while (number>=(n/2.0))
        {
            number --;
            temp ++;
            counter ++;
        }
    }
    else if (number==1)
    {
        counter ++;
        return 0;
    }

    sum(n-1, 1,counter);

    return 0;
}

int main()
{
    int counter=1;
    double number;

    cout << "-------------------------------------------------------\n"
         << "Please enter the number: ";

    cin >> number ;
    cout << "\n";

    if (number!=1)
    {
        sum(number, 1, counter);
    }


    cout << "The total number of combinations that result in a sum of "
         << number << " is: " << counter
         << "\n-------------------------------------------------------\n";

    return 0;
}

Answer 1

I read wiki article you pointed out, they give some instructions how to build recursive defined function. It looks different then your code. The code below works for me

#include <iostream>

using namespace std;

int sum(int k, int n)
{
    if(k == 1 || n == 1)
        return 1;

    if(k < n)
        return sum (k, k);
    else if (k == n)
        return 1 + sum (k, k-1);
    else
        return sum (k,n-1) + sum (k-n, n);
}

int main (void)
{
    int counter=1;
    double number;

    cout << "-------------------------------------------------------\n"
         << "Please enter the number: ";

    cin >> number ;
    cout << "\n";

    counter = sum(number, number);

    cout << "The total number of combinations that result in a sum of "
         << number << " is: " << counter
         << "\n-------------------------------------------------------\n";

    return 0;
}

You can test this code here