Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.08.02
  • Accepted : 2020.01.23
  • Published : 2020.07.31
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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.

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References

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