Find the total number of unique combinations for input values of x = 4 and n = 12
There exists a set of values, r, with values binary increasing (2^0, 2^1, ... 2^(n-1))
A combination is a set of x values where each value is generated by creating x subsets of r with all values within a subset being summed
The x subsets should use all values in r exactly once.
 
Example Case:
Input:
x = 3
n = 5
 
Given the input above we can create a set r that consists of the following n values
[2^0, 2^1, 2^2, 2^3, 2^4]
OR
[1, 2, 4, 8, 16]
 
Each combination is formed via x subsets of the set [1, 2, 4, 8, 16]
[16], [2,8], [1, 4]
[1, 2, 4], [8], [16]
[1, 4], [2, 8], [16]
...
 
This renders sets of size x that are the sums of the elements of each set
16, 10, 5
7, 8, 16
5, 10, 16
...
 
Note: combination 1 and combination 3 are the duplicates and should not be counted twice as they both consist of 5, 10, and 16
 
All possible unique combinations for x = 3 and n = 5:
3   8   20
4   8   19
1   12  18
4   9   18
5   8   18
2   12  17
4   10  17
6   8   17
1   14  16
2   13  16
3   12  16
4   11  16
5   10  16
6   9   16
7   8   16
1   2   28
1   4   26
2   4   25
1   6   24
2   5   24
3   4   24
1   8   22
2   8   21
1   10  20
2   9   20
 
Final Output:
25
(There are 25 combinations generated above)
 
*IMPORTANT*
The answer should be formatted as rgbctf{[output value here]} with your output value replacing [output value here]