Results 31 to 40 of about 717 (218)
On the generalized p-periodic linear recursive sequences via the Fibonacci–Horner decomposition of the matrix powers [PDF]
Notes on Number Theory and Discrete MathematicsIn 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 +2 more
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On the sum of the reciprocals of k-generalized Fibonacci numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 In this note, we that if {Fn(k)}n≥0{\left\{ {F_n^{\left( k \right)}} \right\}_{n \ge 0}} denotes the k-generalized Fibonacci sequence then for n ≥ 2 the closest integer to the reciprocal of ∑m≥n1/Fm(k)\sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}} is
Alahmadi Adel, Luca Florian
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Diophantine Triples and k-Generalized Fibonacci Sequences [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Clemens Fuchs +3 more
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Some properties and extended Binet’s formula for the class of bifurcating Fibonacci sequence
Ratio MathematicaOne of the generalizations of Fibonacci sequence is a -Fibonacci sequence, which is further generalized in several other ways, some by conserving the initial conditions and others by conserving the related recurrence relation.
Daksha Manojbhai Diwan +2 more
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Weighted sum of the sixth powers of Horadam numbers [PDF]
Notes on Number Theory and Discrete MathematicsOhtsuka and Nakamura found simple formulas for Σⁿⱼ₌₁Fⱼ⁶ and Σⁿⱼ₌₁Lⱼ⁶, where Fₖ and Lₖ are the k-th Fibonacci and Lucas numbers, respectively. In this note we extend their results to a general second order sequence by deriving a formula for Σⁿⱼ₌₁(-1/q³ ...
Kunle Adegoke +2 more
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Generalization of the Distance Fibonacci Sequences
AxiomsIn 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 Seyma Yilmaz +2 more
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On Matrix‐Based Cryptography Using Matrix Norm and Special Integer Sequences
Mathematische Nachrichten, EarlyView.ABSTRACT In this paper, a novel matrix‐based encryption approach based on the Affine Hill cipher is presented. The key matrix is constructed using the Narayana integer sequence, and the Frobenius norm of the key matrix is used as a scaling factor in the key construction.
Melih Göcen +1 more
wiley +1 more source
The mathematics of generalized Fibonacci sequences: Binet's formula and identities [PDF]
Mathematica MoravicaThis article considers a generalized Fibonacci sequence {Vn} with general initial conditions, V0 = a, V1 = b, and a versatile recurrence relation Vn = pVn-1 + qVn-2, where n ≥ 2 and a, b, p and q are any non-zero real numbers. The generating function and
Verma K.L.
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Single‐Shot 2D Radial Echo Planar Imaging for Functional MRI
Magnetic Resonance in Medicine, EarlyView.ABSTRACT Purpose To develop a novel single‐shot radial echo planar imaging (ss‐rEPI) technique for rapid, distortion‐free brain imaging in functional MRI experiments. Methods Radial multi‐gradient echo (radial mGRE) data were acquired on a 3T clinical scanner using a 2D ss‐rEPI readout with small golden‐angle rotations between echoes.
Christoph A. Rettenmeier +4 more
wiley +1 more source
Generalized Fibonacci Sequences Generated from a $k$--Fibonacci Sequence
Journal of Mathematics Research, 2012 In this paper we will prove that all $k$--Fibonacci sequence contains generalized Fibonacci sequences and we will indicate the form of obtain them.
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