I am copying (translating to Processing) an algorithm taken from:

http://www.numericana.com/answer/numbers.htm#partitions (the much faster one),

but I am getting the wrong results.

I should get p(n)=  1, 2, 3, 5, 7, 11, 15, 22,  ...

but I get:   2, 6, 16, 44, 123, 340, 947, 2628, ...

What is wrong with my code? or is it the algorithm?

 

int pn(int n) {
  // counting partition(n)
  int[] p = new int[n+1];
  p[0] = 1;
  for (int i=1; i<=n; i++) {
    int j=1;
    int k=1;
    int s=0;
    while (j>0) {
      j = i-(3*k*k+k)/2;
      if (j>=0) {
        s = s - ((-1)^k)*p[j];
      }
      j = i-(3*k*k-k)/2;
      if (j>=0) {
        s = s - ((-1)^k)*p[j];
      }
      k = k+1;
    }
    p[i] = s;
  }
  return p[n];
}