The differences between each pair have the sequence 1, 3, 5, 7,...
The sum of these are the squares of the natural numbers: 1, 4, 9, 16,...
Take the first few of numbers in the series: -5, -4, -1, 4.
-5+0=-5; -5+1=-4, -5+4=-1, -5+9=4.
So the nth term is -5+(n-1)². We could use this formula.
We can expand this. -5+n²-2n+1=n²-2n-4, so we could use this equivalent formula. Example: put n=7, then we have -5+36=31, or 49-14-4=31 as the 7th term.