Distribution Generated by a Random Inhomogenous Fibonacci Sequence

Let G 0 = 0 and G 1 = 1 . The present study deals with the inhomogeneous version G n = G n - 1 + G n - 2 + w n - 2 of the Fibonacci sequence, where w n - 2 takes value a with probability p , and does value b with 1 - p . We describe the probability distribution of the values of G n with fixed n , an...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 21; no. 1
Main Authors Liptai, Kálmán, Szalay, László
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2024
Springer Nature B.V
Subjects
Fibonacci numbers
Mathematics
Mathematics and Statistics
Sequences
05C10
60C05
random inhomogeneous recurrence
11Y55
Fibonacci sequence
discrete distribution
05A15
11B37
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Summary:Let G 0 = 0 and G 1 = 1 . The present study deals with the inhomogeneous version G n = G n - 1 + G n - 2 + w n - 2 of the Fibonacci sequence, where w n - 2 takes value a with probability p , and does value b with 1 - p . We describe the probability distribution of the values of G n with fixed n , and examine the properties like expected value and variance. The most challenging feature is the fractal-like structure of the distribution.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-023-02563-3