This is OK, but I'm not sure it's exactly what is wanted, because there's still a term in the equation.
How about this? The sequence is
-1, 2, 1, 4, 3, 6, 5, 8, ...
which is really just two sequences interwoven. In each of the separate sequences, each term is 2 more than its predecessor. So you can simply write the recurrence relation: