Applications of Fibonacci Numbers : Volume 7

Table of Contents

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   Book Overview
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   Chapter 1 Higher Order Bernoulli Polynomials and Newton Polygons
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   Chapter 2 The Fibonacci Shuffle Tree
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   Chapter 3 On The Period of Sequences Modulo a Prime Satisfying A Second order Recurrence
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   Chapter 4 Generalizations to Large Hexagons of The Star of David Theorem with Respect to Gcd
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   Chapter 5 Longest Success and Failure Runs and New Polynomials Related to The Fibonacci-Type Polynomials of Order k
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   Chapter 6 A Note on a Representation Conjecture By Hoggatt
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   Chapter 7 Some Remarks on The Distribution of Subsequences of Second Order Linear Recurrences
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   Chapter 8 A Criterion For Stability of Two-Term Recurrence Sequences Modulo Odd Primes
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    Chapter 9 A Problem of Diophantus and Pell Numbers
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    Chapter 10 On the Exceptional Set in the Problem of Diophantus and Davenport
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    Chapter 11 Substitutive Numeration Systems and A Combinatorial Problem
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    Chapter 12 A Note on Derived Linear Recurring Sequences*
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    Chapter 13 Observations from Computer Experiments on An Integer Equation
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    Chapter 14 Some Probabilistic Aspects of the Zeckendorf Decomposition of Integers
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    Chapter 15 First Derivative Sequences of Extended Fibonacci and Lucas Polynomials
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    Chapter 16 Elements of Zeckendorf Arithmetic
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    Chapter 17 Binomial Coefficients Generalized with Respect to a Discrete Valuation
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    Chapter 18 The Dying Fibonacci Tree
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    Chapter 19 Smallest Integral Combinatorial Box
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    Chapter 20 New Aspects of Morgan-Voyce Polynomials
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    Chapter 21 Growing a Self-Similar Tree
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    Chapter 22 Lacunary Sums of Binomial Coefficients
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    Chapter 23 Some Reciprocal Summation Identities with Applications to the Fibonacci and Lucas Numbers
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    Chapter 24 A Relative Rank Function on Sets of Continued Fractions Having Bounded Partial Quotients
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    Chapter 25 On Sums of the Reciprocals of Prime Divisors of Terms of a Linear Recurrence
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    Chapter 26 A Fibonacci-Fractal: A Bicolored Self-Similar Multifractal
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    Chapter 27 A Generalisation of Ratios of Fibonacci Numbers with Application to Numerical Quadrature
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    Chapter 28 The Fibonacci Pyramid
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    Chapter 29 On a Three Dimensional Approximation Problem
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    Chapter 30 Analysis of the Euclidean and Related Algorithms
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    Chapter 31 Fundamental Solutions of u 2 -5 v 2 = -4 r 2
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    Chapter 32 Probable Prime Tests Using Lucas Sequences
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    Chapter 33 On a Functional Equation Associated with the Fibonacci Numbers
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    Chapter 34 Diophantine Properties of Linear Recursive Sequences I
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    Chapter 35 The Cantor-Fibonacci Distribution
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    Chapter 36 On the Parity of Certain Partition Functions
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    Chapter 37 There Are Infinitely Many Arithmetical Progressions Formed By Three Different Fibonacci Pseudoprimes
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    Chapter 38 On MikolÁs’ Summation Formula Involving Farey Fractions
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    Chapter 39 Second Order Linear Recurring Sequences in Hypercomplex Numbers
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    Chapter 40 The Bell Differential Polynomials
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    Chapter 41 On Lucas d-Pseudoprimes
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    Chapter 42 Asymmetric Cell Division: Binomial Identities for Age Analysis of Mortal vs. Immortal Trees
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    Chapter 43 The Golden Section and Modern Harmony Mathematics
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    Chapter 44 Lucas Factors and a Fibonomial Generating Function
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    Chapter 45 Elementary Properties of Canonical Number Systems in Quadratic Fields
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    Chapter 46 Three Examples of Triangular Arrays with Optimal Discrepancy and Linear Recurrences
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    Chapter 47 A Multivariate Inverse Polya Distribution of Order k Arising in the Case of Overlapping Success Runs
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    Chapter 48 Introduction to a Fibonacci Geometry
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    Chapter 49 Taylor Functionals and the Solution of Linear Difference Equations
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    Chapter 50 Section — Invariant Numbers and Generalised Golden Section Optimization Algorithms*