Relative growth of the partial sums of certain random Fibonacci-like sequences
نویسندگان
چکیده
منابع مشابه
On the Integrity of Certain Fibonacci Sums
[n is an arbitrary natural number, r is an arbitrary (nonzero) real quantity) gives & positive integer k. Since both r and k turn out to be Fibonacci number ratios, the results established in this paper can be viewed as a particular kind of Fibonacci identities that are believed to be new [see (4.7) and (4.8)]. Throughout the paper we shall make use of the following properties of the Fibonacci ...
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Numerous writers appear to have been fascinated by the many interesting summation identitites involving the Fibonacci and related Lucas numbers. Various types of formulas are discussed and various methods are used. Some involve binomial coefficients [2 ] , [4 ] . Generating function methods are used in [2] and [5] and higher powers appear in [6] . Combinations of these or other approaches appea...
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In this paper, we use ergodic theory to compute the aysmptotic growth rate of a family of random Fibonacci type sequences. This extends the result in [2]. We also prove some Lochs-type results regarding the effectiveness of various number theoretic expansions.
متن کاملThe Asymptotic Growth Rate of Random Fibonacci Type Sequences
Estimating the growth rate of random Fibonacci-type sequences is both challenging and fascinating. In this paper, by using ergodic theory, we prove a new result in this area. Let a denote an infinite sequence of natural numbers {a1, a2, · · · } and define a random Fibonaccitype sequence by f−1 = 0, f0 = 1, a0 = 0, and fk = 2fk−1 + 2fk−2 for k ≥ 1. Then, for almost all such infinite sequences a,...
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2017
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236198.2017.1378353