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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 | |