Results 81 to 90 of about 2,715 (213)

Elementary sequences, sub-Fibonacci sequences

Discrete Applied Mathematics, 1993
A nondecreasing integer sequence \(x_ 1,x_ 2,\dots,x_ k\) with \(x_ 1=x_ 2=1\) and \(n \geq 2\) is said to be elementary if for all \(k \leq n\) \((x_ k>1 \Rightarrow x_ k=x_ i+x_ j\) for some \(i \neq j)\) and sub- Fibonacci if for all \(k \in \{3,\dots,n\}\) \((x_ k \leq x_{k-1}+x_{k- 2})\).
Fishburn, Peter C., Roberts, Fred S.
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Generalization of the Distance Fibonacci Sequences

Axioms
In this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties ...
Nur Şeyma Yilmaz, Andrej Włoch, Engin Özkan   +2 more
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The structure of palindromes in the Fibonacci sequence and some applications [PDF]

, 2016
Yuke Huang, Zhi‐Ying Wen
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Some sums related to the terms of generalized Fibonacci autocorrelation sequences

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2017
In this paper, we give the terms of the generalized Fibonacci autocorrelation sequences defined as and some interesting sums involving terms of these sequences for an odd integer number and nonnegative integers.
Neşe Ömür , Sibel Koparal
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Tantalizing properties of subsequences of the Fibonacci sequence modulo 10 [PDF]

, 2021
Dan Guyer, Aba Mbirika, Miko Scott
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On the generalized p-periodic linear recursive sequences via the Fibonacci–Horner decomposition of the matrix powers [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, we investigate the matrix formulation of the generalized p-periodic linear recursive sequences. To reach our goal, we consider the properties of the Fibonacci–Horner decomposition of the matrix powers and those of the weighted linear ...
Mustapha Rachidi, László Szalay, Fatih Yilmaz   +2 more
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(±1)-Invariant sequences and truncated Fibonacci sequences

Linear Algebra and its Applications, 2005
Let \(P\) and \(D\) denote the Pascal matrix \(\bigl[\binom{i}{j}\bigr]\), (\(i,j=0,1,2,\dots\)) and the diagonal matrix \(\text{diag}((-1)^0,(-1)^1,(-1)^2,\dots)\), respectively. An infinite-dimensional real vector \(\mathbf x\) is called a \(\lambda\)-invariant sequence if \(PD\mathbf x=\lambda\mathbf x\).
Choi, Gyoung-Sik, Hwang, Suk-Geun, Kim, Ik-Pyo, Shader, Bryan L.   +3 more
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Psychoacoustic Properties of Fibonacci Sequences

Acta Polytechnica, 2008
1202, Fibonacci set up one of the most interesting sequences in number theory. This sequence can be represented by so-called Fibonacci Numbers, and by a binary sequence of zeros and ones.
J. Sokoll, S. Fingerhuth
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More generalized k(ε)-Fibonacci sequence, series, and its applications

AIP Advances
In this study, we present a generalized higher-order delta operator with the co-efficient of falling factorial and its inverse, both of which allow us to get more generalized k(ε)-Fibonacci sequences along with their sums, a few theorems, and some ...
Rajiniganth P, Aparna T, Ilyas Khan, Suresh K   +3 more
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Recurrence algorithms of waiting time for the success run of length $k$ in relation to generalized Fibonacci sequences [PDF]

, 2022
Jung‐Taek Oh, Chongjin Park, Sung‐Su Kim   +2 more
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