HDU 1028 Ignatius and the Princess III .

Ignatius and the Princess III

Time Limit: 2000/1000 MS (Java/Others)????Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4658????Accepted Submission(s): 3263

"The second problem is, given an positive integer N, we define an equation like this:
??N=a[1]+a[2]+a[3]+...+a[m];
??a[i]>0,1<=m<=N;
My question is how many different equations you can find for a given N.
For example, assume N is 4, we can find:
??4 = 4;
??4 = 3 + 1;
??4 = 2 + 2;
??4 = 2 + 1 + 1;
??4 = 1 + 1 + 1 + 1;
so the result is 5 when N is 4. Note that "4 = 3 + 1" and "4 = 1 + 3" is the same in this problem. Now, you do it!"