Applications of Fibonacci Numbers

Advances in Linear Pixel Shuffling.- Minimal Center Covering Stars with Respect to LCM in Pascal’s Pyramid and its Generalizations.- Multiple Color Version of the Star of David Theorems on Pascal’s Triangle and Related Arrays of Numbers.- Some Remarks on the Distribution of Second Order Recurrences and a Related Group Structure.- Matrices, Recurrent Sequences and Arithmetic.- Vector Linear Recurrent Sequences in Commutative Rings.- Subwords of the Golden Sequence and the Fibonacci Words.- Interesting Arrays Associated with Fibonacci Sequences.- More Applications of a Partition Driven Symmetric Table.- Partial Derivative Sequences of Second-Order Recurrence Polynomials.- The Zeckendorf Decomposition of Certain Classes of Integers.- On The Sum of Consecutive Squares.- Rado Numbers of Fibonacci Sequences and a Problem of S. Rabinowitz.- Rooks on Fibonacci Boards.- Tiling with Cuisenaire Rods.- Hofstadter’s Conjecture for Ayfi-1.- Recursive Properties of Trigonometric Products.- A Synthesis of Certain Polynomial Sequences.- Minmax Sequences for Pell Numbers.- On Dichotomous Complexity of the Fibonacci Tree.- Formulas of Ramanujan Involving Lucas Numbers, Pell Numbers, and Bernoulli Numbers.- Counting Sets of Integers with Various Summation Properties.- Factorial and Binomial Coefficients in Polynomial Rings over Finite Fields.- An Identity Involving the q-Factorial.- Gcd Properties of an Octagon.- Products and Quotients of Difference Equations.- The Wythoff and the Zeckendorf Representations of Numbers are Equivalent.- Some Basic Translational Properties of the General Fibonacci Line-Sequence.- Pentagonal Numbers in Fibonacci Sequence.- On Reciprocal Sums of Second Order Sequences.- Solving Linear Recurrences from Differential Equations in the Exponential Manner andVice Versa.- The Rational Heart of Integer Fibonacci Pentagons.- Algorithmic Manipulation of Fibonacci Identities.- On Lucas Pseudoprimes of the Form Ax2 + Bxy + Cy2.- On Certain Rational Expressions whose Prime Divisors are Cubic Residues (Mod P).- A Search for Solutions of a Functional Equation.- A Use of Generalized Fibonacci Numbers in Finding Quadratic Factors.- Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P-III.- Divisibility of Terms in Lucas Sequences of the Second Kind by their Subscripts.- On a Model of the Modular Group.- Properties of a k-Order Linear Recursive Sequence Modulo m.- Residue Counts Modulo Three for the Fibonacci Triangle.- On a Class of Congruences for Lucas Sequences.