C/C++ :: Changing Complexity From O(n) To O(1)

For the following code :

 s = 0 ;
 for(i=m ; i<=(2*n-1) ; i+=m) {
            if(i<=n+1)
            { s+=(i-1)/2 ; }
           else
            { s+=(2*n-i+1)/2 ; }  
      }  

I want to change the complexity of the code from O(n) to O(1) . So I wanted to eliminate the for loop . But as the sum "s" stores values like (i-1)/2 or (2*n-i+1)/2 so eliminating the loop involves tedious calculation of floor value of each (i-1)/2 or (2*n-i+1)/2 . It became very difficult for me to do so as I might have derived the wrong formula in sums of floors . Need Changing complexity from O(n) to O(1). Is there any other way to reduce the complexity ? If yes ... then how ?