Just think of an increasing sequence. The program caculates n+1 times for an increasing sequence with n elements. And then divide it into two subsequences. One is the leftmost element, and anthoer is the left elements. It ends at the length of sequence is 2. Thus, the sum is (n+1) + n + (n-1) + ... + 3 = (n+4)(n-1)/2 = (n*n + 3*n - 4)/2. So output 1 to n is ok.