[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b190723

ON CONDITIONALLY DEFINED FIBONACCI AND LUCAS SEQUENCES AND PERIODICITY

Irby, Skylyn (Department of Mathematics University of Alabama)
Spiroff, Sandra (Department of Mathematics University of Mississippi)

Publication Information

Bulletin of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 1033-1048 More about this Journal

Abstract

We synthesize the recent work done on conditionally defined Lucas and Fibonacci numbers, tying together various definitions and results generalizing the linear recurrence relation. Allowing for any initial conditions, we determine the generating function and a Binet-like formula for the general sequence, in both the positive and negative directions, as well as relations among various sequence pairs. We also determine conditions for periodicity of these sequences and graph some recurrent figures in Python.

Keywords

Generalized Fibonacci; linear recurrence; periodicity;

Citations & Related Records

Reference

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