比利时vs摩洛哥足彩
,
university of california san diego
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abacus
sam spiro
university of california, san diego
slow fibonacci walks
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 $n,n,2n,\ldots$. 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 more general recurrence relations. this is joint work with fan chung and ron graham.
october 12, 2021
12:30 pm
zoom -- email jmoneill@ucsd.edu for link
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