Can I prevent down-fill from incrementing *every* cell reference in a formula?

Question

I have a spreadsheet with rows of data. At the end of each row I have a formula that computes a useful number based on (1) the row and (2) some constant cells elsewhere in the sheet. When I add new rows I use down-fill to create the formula cell at the end of each row. However, down-fill increments the references for both the row AND for the constant cells. This results in broken or meaningless references that I need to fix by hand. My alternative is to copy and manually adjust the formula every time I add a new row, which is very tedious. Can I somehow indicate that some cell references in the formula should be incremented when down-filling while others should not?

KarlS · Accepted Answer

You got it. I don't think there is any specific Sheets documentation but here are my cliff notes of how to use them in case others come across this post later.
 
Absolute vs Relative references (or why do I keep seeing $ signs?)
 
Normally when you copy a cell with a formula or drag a formula down or across a page all of the cell references (ranges) in that cell will be adjusted based on the cell starting position and the ending or current position. So a formula in Cell A1 that says "=C1" when copied to cell A2 will change to "=C2" and when copied to B3 will change to "=D3". For every one column over the letter increments by one and for every row down the number increases by one. This is relative referencing.  
 
Absolute references (using the $ sign) are for when you want a cell reference (the column, the row, or both) to remain constant when copying the formula to another cell or dragging a cell down a row. You use a $ sign in front of the part that you want to remain constant, $A1 = constant column, A$1 = constant row, $A$1 = fixed position. You can quickly rotate through the various possibilities using the F4 function key. (On some computers, you may need to hold Fn and press the function key for it to work.)
Edit: Note that if you INSERT or DELETE a column/row it will change references so that they still refer to the same cell even if both the row and column are set using $. For example, if a reference points to column D and then a column is inserted between B and C, the original column D will move over and become column E. The reference will now point to column E instead of D.
 
If you would like a more detailed response, here is good reference with more details.

Calvin Loncaric · Accepted Answer

I think I figured it out: this can be done by using "absolute" rather than "relative" references. More information in this tutorial:
https://yagisanatode.com/2017/11/01/how-do-i-lock-certain-cells-in-a-formula-in-google-sheets/
I was not able to find any information about this in the official Google Sheets documentation, but it is also a feature in Microsoft Excel and I guess there is a lot of overlap.