AN ANALYSIS OF THE SEQUENCE Xn+2 = i m Xn+1 + Xn

Authors

David Duncan, Coastal Carolina UniversityFollow
Prashant Sansgiry, Coastal Carolina UniversityFollow
Ogul Arslan, Coastal Carolina UniversityFollow
Jensen Meade, Coastal Carolina UniversityFollow

Abstract

We analyze the sequence Xn+2 = imXn+1 + Xn, with X1 = X2 = 1 + i, where i is the imaginary number and m is a real number. Plotting the sequence in the complex plane for different values of m, we see interesting figures from the conic sections. For values of m in the interval (−2, 2) we show that the figures generated are ellipses. We also provide analysis which prove that for certain values of m, the sequence generated is periodic with even period.

Recommended Citation

Duncan, David; Sansgiry, Prashant; Arslan, Ogul; and Meade, Jensen (2023) "AN ANALYSIS OF THE SEQUENCE Xn+2 = i m Xn+1 + Xn," Journal of the South Carolina Academy of Science: Vol. 21: Iss. 2, Article 2.
Available at: https://scholarcommons.sc.edu/jscas/vol21/iss2/2