Sam Spiro, University of California, San Diego

Abstract

We define a Fibonacci walk to be any sequence of positive integers satisfying the recurrence w_{k+2} = w_{k+2} = w_{k+1}+w_k, and we say that a sequence is an n-Fibonacci walk if w_k = n for some k. Note that every $n$ has a number of boring n-Fibonacci walks, e.g. the sequence starting n, n, 2n, ... . To make things interesting, we consider n-Fibonacci walks which have w_k=n with k as large as possible, and we call this an n-slow Fibonacci walk. For example, the two 6-slow Fibonacci walks start 2, 2, 4, 6 and 4, 1, 5, 6. In this talk we discuss a number of properties about n-slow Fibonacci walks, such as the number of slow walks a given $n$ can have, as well as how many n have a given number of walks. We also discuss slow walks that follow other recurrence relations.

This is joint work with Fan Chung and Ron Graham.

SPECIAL NOTE: This seminar is presented online only.

You can join via ZOOM with Meeting ID: 268 276 468 or by clicking this link https://brown.zoom.us/j/268276468

For further information see: https://sites.google.com/view/gocc-combinatorics/home