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List of Symbols xiii ; Preface xv ; 31. Fibonacci and Lucas Polynomials I 1 ; 31.1. Fibonacci and Lucas Polynomials 3 ; 31.2. Pascal's Triangle 18 ; 31.3. Additional Explicit Formulas 22 ; 31.4. Ends of the Numbers l n 25 ; 31.5. Generating Functions 26 ; 31.6. Pell and Pell-Lucas Polynomials 27 ; 31.7. Composition of Lucas Polynomials 33 ; 31.8. De Moivre-like Formulas 35 ; 31.9. Fibonacci-Lucas Bridges 36 ; 31.10. Applications of Identity (31.51) 37 ; 31.11. Infinite Products 48 ; 31.12. Putnam Delight Revisited 51 ; 31.13. Infinite Simple Continued Fraction 54 ; 32. Fibonacci and Lucas Polynomials II 65 ; 32.1. Q-Matrix 65 ; 32.2. Summation Formulas 67 ; 32.3. Addition Formulas 71 ; 32.4. A Recurrence for f n 2 76 ; 32.5. Divisibility Properties 82 ; 33. Combinatorial Models II 87 ; 33.1. A Model for Fibonacci Polynomials 87 ; 33.2. Breakability 99 ; 33.3. A Ladder Model 101 ; 33.4. A Model for Pell-Lucas Polynomials: Linear Boards 102 ; 33.5. Colored Tilings 103 ; 33.6. A New Tiling Scheme 104 ; 33.7. A Model for Pell-Lucas Polynomials: Circular Boards 107 ; 33.8. A Domino Model for Fibonacci Polynomials 114 ; 33.9. Another Model for Fibonacci Polynomials 118 ; 34. Graph-The

Author

Koshy, Thomas

Publisher

John Wiley & Sons, Incorporated

Published

2018

Language

EN

ISBN

9781118742143