Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Non-linear recurrences which unexpectedly produce rational numbers

Speaker: **Emilie Hogan**, Rutgers University

Date: Thursday, March 4, 2010 5:00pm

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

Abstract:

Non-linear recurrences which generate integers have been widely studied (e.g., the Somos recurrences). Typically these recurrences are linear in the highest order term. In this talk I will investigate what happens when we remove this restriction. We no longer produce single sequences given some initial conditions but an infinite set of sequences. Additionally we expect irrational numbers. I will show some examples of these types of recurrences which produce rational numbers and discuss how they were discovered.