Coding the algorithm you mentioned in your comment, in pseudo VB code:
ReDim result(2 ^ (Length of Array) - 1)
for index = 0 to 2 ^ (Length of Array) - 1
sum = 0
for counter = 0 to (Length of Array) - 1
If ((2 ^ counter) And index) <> 0 Then
sum += Array(counter+1)
result(index) = sum