کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6422209 | 1340618 | 2011 | 9 صفحه PDF | دانلود رایگان |
Consider the generalized Fibonacci sequence {qn}n=0â having initial conditions q0=0,q1=1 and recurrence relation qn=aqn-1+qn-2 (when n is even) or qn=bqn-1+qn-2 (when n is odd), where a and b are nonzero real numbers. These sequences arise in a natural way in the study of continued fractions of quadratic irrationals and combinatorics on words or dynamical system theory. Some well-known sequences are special cases of this generalization. The Fibonacci sequence is a special case of {qn} with a=b=1. Pell's sequence is {qn} with a=b=2 and the k-Fibonacci sequence is {qn} with a=b=k. In this article, we study numerous new properties of these sequences and investigate a sequence closely related to these sequences which can be regarded as a generalization of Lucas sequence of the first kind.
Journal: Applied Mathematics and Computation - Volume 217, Issue 12, 15 February 2011, Pages 5603-5611