Unbounded Integer Sequences (A n ) n≥0 with A n+1A n−1− A n 2 Bounded are of Fibonacci Type

Andreas Dress () and Florian Luca ()
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Andreas Dress: Bielefeld University, Mathematics Department
Florian Luca: Bielefeld University, Mathematics Department

A chapter in Algebraic Combinatorics and Applications, 2001, pp 102-109 from Springer

Abstract: Abstract It is well known that the Fibonacci sequence (F n ) n ≥0 defined by F0 = 0, F1 = 1, and F n +2 = n +1 +F n for all n ≥ 0 satisfies the condition F2 n − F n +1 F n −1 = (-1) n for all n ∈ N In this note, we show that — somehow conversely — if (A n ) n ≥0 is a sequence of integers such that (|A n |) n ≥0 diverges to infinity and |A2 n − A n +1 A n −1|remains bounded, then (A n ) n ≥0 is binary recurrent from some n on. An application to real quadratic units is also presented.

Keywords: real quadratic units; binary recurrent sequences; Fibonacci sequences (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-3-642-59448-9_7

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