You have landed on the planet Alpha Seventy populated by a people named the Dymey. While visiting, you are befriended by a Dymey named Z. Z explains their rich history, culture, and physiology. Interestingly, the Dymey reproduce asexually and only once in their lifetime. Specifically at age 25, a Dymey person hatches exactly two offspring. These are the only two offspring hatched in the lifetime of any Dymey. The Dymey live to exactly 100 years before they ascend to the next plane of existence. This gets you thinking about Z descendants and ancestors.

You leave Alpha Seventy right after Z hatches their first set of offspring and return to Earth. Later you are given an opportunity to return to Alpha Seventy. Between the travel and the temporal vortex around the planet you arrive at an unspecified time in the future since your last visit. You survey all of Zs descendants that just hatched in the most recent cycle. Assuming you have found n recently hatched. How many unascended descendants of Z are on the planet? State your findings in terms of n and prove it by induction.