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Fibonacci and Lucas Numbers with Applications
Preface. List of Symbols. Leonardo Fibonacci. The Rabbit Problem. Fibonacci Numbers in Nature. Fibonacci Numbers: Additional Occurrances. Fibonacci and Lucas Identities. Geometric Paradoxes.Expand
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Catalan Numbers with Applications
1. Bionomial Coefficients 2. The Central Binomial Coefficient 3. The Central Binomial Coefficient Revisited 4. Binomial Coeffiecients Revisited 5. Catalan Numbers 6. The Ubiquity of Catalan Numbers IExpand
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Elementary Number Theory with Applications
Fundamentals Divisibility Theory Canonical Decompositions Linear Diophantine Equations and Congruences Congruences Applications Systems of Linear Congruences Three Classical Milestones MultiplicativeExpand
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Pell and Pell–Lucas Numbers with Applications
Preface.- List of Symbols.- Abbreviations.- 1. Fundamentals.- 2. Pell's Equation.- 3. Continued Fractions.- 4. Pythagorean Triples.- 5. Triangular Numbers.- 6. Square-Triangular Numbers.- 7. Pell andExpand
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Triangular Arrays with Applications
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Ternary Words and Jacobsthal Numbers
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Parity and Primality of Catalan Numbers
Catalan numbers, like Fibonacci and Lucas numbers, appear in a variety of situ ations, including the enumeration of triangulations of convex polygons, well-formed sequences of parentheses, binaryExpand
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GRAPH-THEORETIC MODELS FOR THE UNIVARIATE FIBONACCI FAMILY
We construct graph-theoretic models for an extended univariate Fibonacci family, which includes Fibonacci, Lucas, Pell, and Pell-Lucas polynomials.
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Gaussian Fibonacci and Lucas Numbers
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Convergence of a Catalan Series
Summary This article studies the convergence of the infinite series of the reciprocals of the Catalan numbers. We extract the sum of the series as well as some related ones, illustrating the power ofExpand
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