Periodic Coefficients and Random Fibonacci Sequences
نویسندگان
چکیده
منابع مشابه
Periodic Coefficients and Random Fibonacci Sequences
The random Fibonacci sequence is defined by t1 = t2 = 1 and tn = ±tn−1 + tn−2, for n > 3, where each ± sign is chosen at random with probability P (+) = P (−) = 12 . Viswanath has shown that almost all random Fibonacci sequences grow exponentially at the rate 1.13198824 . . . . We will consider what happens to random Fibonacci sequences when we remove the randomness; specifically, we will choos...
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The notion of an∞-generalized Fibonacci sequence has been introduced in [6], and studied in [1], [7], [9]. This class of sequences defined by linear recurrences of infinite order is an extension of the class of ordinary (weighted) r-generalized Fibonacci sequences (r-GFS, for short) with r finite defined by linear recurrences of r order (for example, see [2], [3], [4], [5], [8] etc.) More preci...
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We study the random Fibonacci tree, which is an infinite binary tree with non-negative numbers at each node defined as follows. The root consists of the number 1 with a single child also the number 1. Then we define the tree recursively in the following way: if x is the parent of y, then y has two children, namely |x−y| and x+y. This tree was studied by Benoit Rittaud [?] who proved that any pa...
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We study the random Fibonacci sequences defined by F 1 = F 2 = e F 1 = e F 2 = 1 and for n ≥ 1, F n+2 = F n+1 ± Fn (linear case) and e F n+2 = | e F n+1 ± e Fn| (non-linear case), where each ± sign is independent and either + with probability p or − with probability 1 − p (0 < p ≤ 1). Our main result is that the exponential growth of Fn for 0 < p ≤ 1, and of e Fn for 1/3 ≤ p ≤ 1 is almost surel...
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Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence . It is shown that this sequence is periodic with the period ( ) if | | .
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/3204