A fib sequence can be defined corecursively using unfold and its actually a nice way to write it in some languages.

Here is the next fib in a sequence (in psuedocode):

     (a, b) -> (a, (b, a+b))

And then you can get a sequence with unfold by giving it some starting numbers:

    val fibonacci: Iterator[Int] =
      Iterator.unfold((1, 1)) {
        case (x, y) => Some((x, (y, x + y)))
      }

(That is Scala. But lots of languages have an unfold method)

    > fibonacci.take(8).toList 
    1, 1, 2, 3, 5, 8, 13, 21