Assume there are numbers typed in range B3:G8. In row 10, one may want to sum up diagonal cells i.e. in cell B10, one would want to get the value from cell B8, in cell C10, one may want to sum values from cells B7 and C8. in cell D10, one may want to sum values from cells B6, C7 and D8 and so on.
You may refer to my solution in this workbook.