A simplified explanation of this editorial is required

Hi All!
Although I was able to solve this problem using pattern-building methods, I am intrigued by the editorial, too and want to be able to code the solution in that manner, too.
The following is the editorial to the problem ODD ARRAY, which I have been having difficulty comprehending.

If anyone can simplify it and help me understand, would be of great help!
-Aamod Vardhan Pandey