We get a bunch of consecutive values

x |  y
1 | -1
2 |  1
3 |  3
4 |  5
5 |  7
6 |  9
. |  .
. |  .
. |  .

We observe

1.  That we start with the first term a1=-1

We also observe

2.  That we add 2 to each term to get the next term.

Therefore, the recursion equation is

a1 = -1,  an = an-1 + 2 for n > 2

Edwin