On conditionally defined Fibonacci and Lucas sequences and periodicity
Bull. Korean Math. Soc. 2020 Vol. 57, No. 4, 1033-1048
Published online February 27, 2020
Printed July 31, 2020
Skylyn Irby, Sandra Spiroff
University of Alabama; University of Mississippi
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 {\it Python}.
Keywords : Generalized Fibonacci, linear recurrence, periodicity
MSC numbers : Primary 11B39, 15A06
Supported by : S.~Spiroff is supported by Simons Foundation Collaboration Grant \#584932
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