As Kyle indicates, people would typically just use relative addressing, and his answer describes how to do that. You can see how simple the formulas become.
Explanation of original formulas
The sample formulas you included in the question may have been done that way to highlight the relationship between the cell addresses. As long as the structure doesn't change, that style of addressing focuses on the logic of the physical relationships of the cells. Note, though, that if the structure of the spreadsheet changes, everything will break down because the references are tied to the original structure.
To understand what they're doing, ADDRESS builds a text description of a cell reference. This lets you use calculations to figure out where a reference should point. A good, brief demo here. INDIRECT converts a text description of a cell reference into an actual reference.
So if you want a cleaner alternative, the cleanest would be to just use actual cell references, like Kyle's answer. If you're in the situation where you actually want the focus on the spreadsheet structure, there are still a few ways to streamline this.
There's a form of addressing called R1C1, that expresses addresses as absolute or relative rows and columns in a way that can be calculated and used directly, without needing the ADDRESS, ROW, and COLUMN functions.
For an absolute address, use row number and column number after the R and C labels. So
A3 would be
For relative addressing, leave off the number to refer to the current row or column, or put the relative number in square brackets. So the cell on the same row and two columns to the left would be referenced as
In both Excel and Calc, there's an option to change the address style to R1C1, which would apply to everything. However, you can use it in specific formulas without doing that by making it a text string and using INDIRECT (which needs the optional addressing style parameter set to zero to recognize the R1C1 style). So the first formula:
You can see that this is sort of a shorthand for the ADDRESS/ROW/COLUMN construction.
The typical way to do this, though, when you need to make the relative relationships obvious, is shorter than this. You can use the OFFSET function. The short form to refer to a single cell is
OFFSET(reference,rows,columns). You specify the starting point and then the number of rows and columns away from it.
In your examples, the formula determines what the current cell is, and you could do that in OFFSET, but it generally isn't necessary. The actual cell reference is typically used. Like in Kyle's answer, that will normally get properly translated if you copy the formula to another cell. OFFSET is a way to make the location relationship explicit. So if your first formula was in cell
C5, it would look like this: