If one iterates the map z -> z^2 + c there is obviously a simple formula for the sequence one gets if c=0. Less obviously, there is also a simple formula when c = -2 (use the identity 2 cos(2x) = (2cos(x))^2 - 2). Are there any other values of c for which one can solve this recurrence explicitly? (For all initial values of course: there are many trivial explicit solutions for special initial values, such as fixed points.)

Related links:
http://en.wikipedia.org/wiki/Mandelbrot_set (the points c where 0 remains bounded under iteration of this map: this strongly suggests that there is no simple exact solution for general c).
http://en.wikipedia.org/wiki/Logistic_map (gives the explicit solutions above, after a change of variable)

Motivation: I once used the map with c=-2 in a lecture to show that one could prove limits exist even without a formula for the exact solution. A first year calculus student pointed out the non-obvious exact solution above, and I don't want to be caught out like this again.