Seminars & Colloquia Calendar

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.