Making a SUM formula with variable sum range

Hi all,

I'm looking for a way to make a SUM formula that shifts it's range (in a non-standard way) when I copy it to other cells.
Each sum has a vertical range above it. The range of the sum 1 column to the right, should start 1 row lower (but end in the same row).
The attached example file will probably make more sense than this explanation

I've experimented with OFFSET, INDIRECT, MID("ABCD...";COLUMN(B3);1) etc etc but I can't get it right...
Who can help me?

Thanks a lot,
Leon