#include<iostream.h>

/* Modifies the previous program sum.cpp.  Now there is an outer loop
   in which sum goes from 0 to 10 by 2's.  Notice that sum must be
   reset to 0 inside the outer loop before the inner loop.  Also note
   the cout line commented out.  This is a helpful debugging tool. */

/* computes the sum 1*(0*0) + 4*(1*1) + 2*(2*2) + 4*(3*3) + 2*(4*4) +
    ... + 2*(num-2)*(num-2) + 4*(num-1)*(num-1) + 1*(num*num), where
   num is a positive even integer.  (This sort of sum comes up in
   Simpson's rule in calculus.)  If i is a counter variable going from
   0 to num, then the general term in the sum is of the form coeff*i*i, 
   where the coefficient coeff is determined by this rule:
      if i is odd, then coeff = 4
      if i is 0 or i is num, then coeff = 1
      if i is even, and not 0 or num, then coeff = 2 */


void main() {
  
  int num, sum, i, coeff;

  for (num=0; num <= 10; num +=2){
    
    sum = 0;
    
    for (i=0; i<=num; i++){

      if (i%2) coeff = 4;
      else if (i==0 || i==num) coeff = 1;
      else coeff = 2;

      sum += coeff * i*i;
      /*  cout << "i = " << i << ", sum = " << sum << ", coeff = "
	  << coeff << ", num = " << num << endl; */
    }
    cout << "num = " << num << ", sum = " << sum << endl;
  }
}