Ahoy all late nighters. looking for a some clarity on a problem I have. Please go easy. Im sure to screw something up when writing this.

Ok so heres the problem as I know it. It is an algorithm with the following behavior:

which I believe is the following series

Now all the 's are unknown and are an integer in the range 1-26

Given a value for can a unique sum be found? I suspect there will be multiple solutions. Could someone help me simplify this?

If it helps, assume