Applications of Fibonacci Numbers

Multidimensional Golden Means.- A Necessary and Sufficient Condition that Rays of A Star Configuration on Pascal’s Triangle Cover Its Center With Respect to GCD and LCM.- On the Minimal Center Covering Stars With Respect to GCD In Pascal’s Pyramid and Its Generalizations.- An Extension of an Old Classical Diophantine Problem.- Fourier Analysis in Finite Nilpotent Groups.- Wall and Vinson Revisited.- Designer Decimals: Fractions Which Contain Second Order Recursion Sequences in Their Decimal Expansions, Reading Left to Right or Right to Left.- Semigroup Presentations and Number Sequences.- Counting the Number of Solutions of Congruences.- On the Number of Overlapping Success Runs in A Sequence of Independent Bernoulli Trials.- Embedding Fibonacci Words Into Fibonacci Word Patterns.- On Sums of Cubes of Fibonacci Numbers.- Integer Sided Triangles Whose Ratio of Altitude to Base Is an Integer.- On a class of Iterative Recurrence Relations.- Discrete Operational Calculi for Two-Sided Sequences.- Transformations of Fibonacci-Lucas Identities.- Fibonacci Numbers and Continued Fraction Expansions.- The DFF and DFFZ Triangles and Their Mathematical Properties.- Contributions from Cascaded Combinations to the Naming of Special Permutations.- The Zeckendorf Representation of {Fkn/Fn}.- Fractal Patterns Derived from Rational Binomial Coefficients.- Hausdorff Dimension in Pascal’s Triangle.- Chaos, Elliptic Curves and All that.- Co-Related Sequences Satisfying the General Second Order Recurrence Relation.- On the Moments of The Sum-of-Digits Function.- Problems on Fibonacci and B-Adic Tree Representations by Regular K-Gons.- Two-Distance Sets and the Golden Ratio.- A Fibionacci Problem Classification Scheme Useful to Undergraduate Pedagogy.- Zeckendorf Representations ofPositive and Negative Integers by Pell Numbers.- Integration Sequences of Fibonacci and Lucas Polynomials.- Pell-Type Number Generators of Pythagorean Triples.- Balance Morphology of a Binary Tree.- Nörlund’s Number B(n)n.- On Stirling-Type Pairs and Extended Gegenbauer-Humbert-Fibonacci Polynomials.- A Sequence Arising from Reflections in Multiple Glass Plates.- Diophantine Representation of Non-Fibonacci Numbers.- On Some Problems Related to the Fibonacci Group.- Congruence Properties of Fibonacci Numbers and Fibonacci Coefficients Modulo P2.- Orderings of the Set of All Positive Fibonacci Sequences.- Some Results Concerning the Reciprocal Sum of Prime Divisors of a Lucas Number.- Rational Numbers with Predictable Engel Product Expansions.- Two Families of Orthogonal Polynomial Systems Related to Fibonacci Chains.- On the Formation of Higher Order Higher Dimensional Line-Sequential Vector Spaces.- Arithmetic Sequences and Second Order Recurrences.- Generalized Fibonacci Pseudoprimes and Probable Primes.- A Generalization of the Fibonacci Sequence.- How to Advance on a Stairway by Coin Flippings.- Fibonacci Sequence and Its Generalizations Hidden in Algorithms for Generating Morse Codes.- On Matrix Representations of Generalized Fibonacci Numbers and Their Applications.- A Cholesky Decomposition in Matching Insulin Profiles.- Generalized Exponential and Trigonometric Functions.- Divisibility of Terms in Lucas Sequences by Their Subscripts.- Upper Bounds for Frequencies of Elements in Second-Order Recurrences Over a Finite Field.- On the Convergence of Quotients of Some Recursive Sequences.- Two Distribution Problems for Polynomials.- The Elements of Enteger Geometry.- Totient Functions on the Euler Number Tree.- Using Matrix Techniques to Establish Properties ofk-Order Linear Recursive Sequences.