@article{Hachicha2025, 
author = {Skander Hachicha and Najmeddine Attia},
title = {Probabilistic approaches to exploring Binet's type formula for the Tribonacci sequence},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {5},
pages = {11957-11975},
keywords = {Tribonacci sequence, Binet formula, Tribonacci random variable, Markov chain},
url = {https://www.sciopen.com/article/10.3934/math.2025540},
doi = {10.3934/math.2025540},
abstract = {This paper presents a detailed procedure for deriving a Binet's type formula for the Tribonacci sequence    {                    T              n    }. We examine the limiting distribution of a Markov chain that encapsulates the entire sequence    {                    T              n    }, offering insights into its asymptotic behavior. An approximation of                      T              n   is provided using two distinct probabilistic approaches. Furthermore, we study random sequences of the form    {                    Z              0    ,                    Z              1    ,                    Z              2    ,                    Z              n    =                    Z                    n      −      3        +                    Z                    n      −      2        +                    Z                    n      −      1        ,  n  =  3  ,  …  }, referred to as the Tribonacci sequence of Random Variables. These sequences, fully defined by their initial random variables, are analyzed in terms of their distributional and limiting properties.}
}