On the Characterization of Periodic Generalized Horadam Sequences
نویسنده
چکیده
The Horadam sequence is a direct generalization of the Fibonacci numbers in the complex plane, which depends on a family of four complex parameters: two recurrence coefficients and two initial conditions. In this article a computational matrix-based method is developed to formulate necessary and sufficient conditions for the periodicity of generalized complex Horadam sequences, which are generated by higher-order recurrences for arbitrary initial conditions. The asymptotic behavior of generalized Horadam sequences generated by roots of unity is also examined, along with upper boundaries for the disk containing periodic orbits. Some applications are suggested, along with a number of future research directions. 2000 Mathematics Subject Classification: Primary 11B37; Secondary 11B39, 15A24, 40C05.
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On some properties and applications of Horadam sequences
The Horadam sequence is a generalization of the Fibonacci numbers in the complex plane, depending on a family of four complex parameters: two recurrence coefficients and two initial conditions. The necessary and sufficient periodicity conditions formulated in [1] are used to enumerate all Horadam sequences with a given period [2]. The geometry of periodic orbits is analyzed, where regular star-...
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