Hjorthenify

n	f(n)	f'(n)	Estimate
2	0	+2	0
3	2	+2	1.5
4	4	+3	4
5	7	+4	7.5
6	11	+5	12
7	16	+6	17.5
8	22	+7	24
9	29	+8	31.5
10	37	+9	40
f(n) are from observations and I need to find f. After I observed the delta between the values I came to the conclusion that f'(n) = n - 1 after which I then did $\int_{}^{} n -1 dn \rightarrow \frac{(x-2)x}{2}$ as shown in the estimate column. The values are bit off and I can't figure out why. Can someone help? :D

struct float_proxy{
  float v;
  float operator %(float other){
    return fmod(v, other);
  }
};

float_proxy operator ""_f(long double f){
  float_proxy tmp;
  tmp.v = f;
  return tmp;
}

int main(int argc, char ** args){
  cout << 2.0_f%2.0f << endl;
  return 0;
}