### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu
**Nathan Fox**, Rutgers University, fox {at} math [dot] rutgers [dot] edu)

Title: An Exploration of Nested Recurrences Using Experimental Mathematics (thesis defense)

Speaker: **Nathan Fox**, Rutgers University

Date: Monday, March 30, 2017 5:00 pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
Nested recurrence relations, such as the Hofstadter Q-recurrence Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)), have no general theory. Solutions are highly dependent on the initial conditions, and many sequences they generate are not even known to be infinite. In this talk, we will see a variety of results pertaining to sequences arising from nested recurrences. These results include a method of automatically discovering solutions of a particular form, some sequences exhibiting never-before-seen behavior, and methodology for analyzing entire families of initial conditions simultaneously.

See: http://www.math.rutgers.edu/~nhf12/expmath/