Excel Copy formula with row automatically modified

I am trying to figure out a means to copy a formula across multiple columns
so that the row value increments automatically but not the column value. For
example:

The first cell, A1, has a formula of: =Sheet1!K110
After copy/paste, Cell B1 should have: =Sheet1!K114
After copy/paste, Cell C1 should have: =Sheet1!K118
After copy/paste, Cell B1 should have: =Sheet1!K122

The sheet I am working on has probably 200 such cells so being able to do
this via copy/paste would be ideal compared to editing each cell one-by-one.

Try this:

=INDEX(Sheet1!$K110:$K300,COLUMNS($A1:A1)*4-3)

Copy across as needed. Adjust the end of range: $K300 as needed.

Here is another option:

=INDIRECT("Sheet1!K"&106+COLUMN()*4)