A computational perspective on meta-Fibonacci recurrence relations

In that Phd thesis, we explore meta-Fibonacci recurrence relations concept in a new approach thanks to detailed computational investigations that are provided by a computer algebra system PARI/GP. It is well known that nested recurrence relations are considered one of the most resistant subclasses of nonlinear recurrences to known proof techniques of difference equations. In that direction, we introduce and analyse not only selected spesific variants but also certain solution families while we prove their properties based on new types of structural connections between systems of nested recurrence relations. In particular, we provide remarkable computational evidences on the existence of infinitely many different solutions for a notable class of nested recurrences while this is also provable for certain families of slow solutions. Additionally, generational methods for erratic meta-Fibonacci sequences, and related statistical properties of successive generations are studied in the scope of the thesis. Keywords: Hofstadter sequence, Hofstadter-Huber family, nested recurrences