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| Foreword | |
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| Fibonacci Identities | |
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| Combinatorial Interpretation of Fibonacci Numbers | |
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| Identities | |
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| A Fun Application | |
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| Notes | |
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| Exercises | |
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| Gibonacci and Lucas Identities | |
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| Combinatorial Interpretation of Lucas Numbers | |
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| Lucas Identities | |
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| Combinatorial Interpretation of Gibonacci Numbers | |
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| Gibonacci Identities | |
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| Notes | |
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| Exercises | |
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| Linear Recurrences | |
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| Combinatorial Interpretations of Linear Recurrences | |
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| Identities for Second-Order Recurrences | |
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| Identities for Third-Order Recurrences | |
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| Identities for kth Order Recurrences | |
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| Get Real! Arbitrary Weights and Initial Conditions | |
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| Notes | |
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| Exercises | |
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| Continued Fractions | |
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| Combinatorial Interpretation of Continued Fractions | |
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| Identities | |
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| Nonsimple Continued Fractions | |
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| Get Real Again! | |
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| Notes | |
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| Exercises | |
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| Binomial Identities | |
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| Combinatorial Interpretations of Binomial Coefficients | |
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| Elementary Identities | |
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| More Binomial Coefficient Identities | |
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| Multichoosing | |
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| Odd Numbers in Pascal's Triangle | |
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| Notes | |
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| Exercises | |
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| Alternating Sign Binomial Identities | |
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| Parity Arguments and Inclusion-Exclusion | |
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| Alternating Binomial Coefficient Identities | |
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| Notes | |
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| Exercises | |
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| Harmonic and Stirling Number Identities | |
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| Harmonic Numbers and Permutations | |
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| Stirling Numbers of the First Kind | |
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| Combinatorial Interpretation of Harmonic Numbers | |
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| Recounting Harmonic Identities | |
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| Stirling Numbers of the Second Kind | |
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| Notes | |
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| Exercises | |
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| Number Theory | |
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| Arithmetic Identities | |
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| Algebra and Number Theory | |
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| GCDs Revisited | |
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| Lucas' Theorem | |
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| Notes | |
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| Exercises | |
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| Advanced Fibonacci & Lucas Identities | |
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| More Fibonacci and Lucas Identities | |
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| Colorful Identities | |
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| Some "Random" Identities and the Golden Ratio | |
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| Fibonacci and Lucas Polynomials | |
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| Negative Numbers | |
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| Open Problems and Vajda Data | |
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| Some Hints and Solutions for Chapter Exercises | |
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| Appendix of Combinatorial Theorems | |
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| Appendix of Identities | |
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| Bibliography | |
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| Index | |
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| About the Authors | |