A note on generalized Fibonacci sequences

doi:10.1016/j.amc.2010.12.038

A note on generalized Fibonacci sequences

2011-02-01

87

PRE

AI

Y

Yayenie, Omer *

DOI：10.1016/j.amc.2010.12.038

原文链接

原文求助

摘要

En 中文

Consider the generalized Fibonacci sequence {q(n)}(n-0)(infinity) 0 having initial conditions q(0) = 0; q(1) 1 and recurrence relation q(n) = aq(n-1) + q(n-2) (when n is even) or q(n) = bq(n-1) + q(n-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 {q(n)} with a = b= 1. Pell's sequence is {q(n)} with a = b= 2 and the k-Fibonacci sequence is {q(n)} 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. (C) 2010 Elsevier Inc. All rights reserved.

Keyword:

Fibonacci sequence

k-Fibonacci sequence

Generalized Fibonacci sequence

Generating functions

A note on generalized Fibonacci sequences

摘要

AI总结

期刊

机构

引用论文