Recursive Method to Find Total no of ways in which a positive number K can be written as sum of integers smaller than K

consider the a number 5. It can be represented as following sets {1+1+1+1+1},{1+1+1+2},{1+2+2},{1+1+3},{1+4},{2+3},{5+0} hence there are total seven.

recursive solution for finding total no of ways...

T(n) = Sigma (-1)^(m+1)*[ T(n-m*(3*m-1)/2) + T (n-m*(3*m+1)/2)]

where m = 1,2,3.........until (n-m*(3*m+1)/2) > 0;
Example:
T(5) = T(4) +T(3) - T(0)

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          int T(int n)
        {
            if(n <  0)
                return 0;
            else
            {
                if(n == 0)
                    return 1;
                else
                {
                    int temp = 1;
                    int tempr = 0;
                    int m = 0;
                    while(temp  >   0)
                    {
                        m++;
                        temp = n-m*(3*m+1)/2;
                        tempr += pow(-1,m+1)*T(n-m*(3*m-1)/2) +
                                          pow(-1,m+1)*T(n-m*(3*m+1)/2);
                    }
                    return tempr;
                }
            }
        }
         
       int main()
       {
             int number;
             scanf("%d",number;);
             printf("\nTotal ways = %d",T(number));
       } 

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