●TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLE
CHAPTER
1.TRODUCTION
1.1 Rabbit Problem
2.HISTORICAL BACKGROUND
3.FONACCI SEQUENCE
3.1 Fibonaccinumbers innature
3.2 The Fibonacci sequence even shows up in music
3.3 The Fibonacci spiral
3.4 Construction ofFibonacci spiral
3.5 second Order recursive sequences
4.GENERALED FIBONACCI SEQUENCES
5.PROPER.OF GENERALED FIBONACCI SEQUENCE
5.1 Generating function
5.2 Binet's formula
5.3 Limitofthequotientoftwo consecutiveterms
5.4 Catalan's identity
5.5 Cassini's identityor simpson's identity
5.6 docagnes's identity
6.SUM AND DIFFERENCE OF THE SQUARES OF THE EVEN GENERALIZED FIBONACCI NUMBERS
7.IDENTITIES OF GEN.FIBONACCI SEQUENCE
8.CONNECTION FORMULAS
9.ANOTHER IMPORTANT FORMULAE
10.IDENTITIES FOR THE COMMON FACTORS OF GEN.FIBO.,JACO.AND JACOBSTHAL-LUCAS NUMBERS
11.COMBINATORIAL FORMULAS INVOLVING GENERALIZED FIBONACCI SEQUENCE
11.1 series of Combinatorial Identities on φ(n,k)
11.2 series of Combinatorial Identmes on Ck(n)
12.CONCLUSION
13.BIBLIOGRAPHY
編輯手記

本書共包含十三章內容，介紹了數學研究者及工程研究者經常遇到或使用的廣義斐波那契數列，通過大量的文獻證明了斐波那契數的普遍性。本書首先由兔子問題引入，介紹了斐波那契數列的歷史背景，然後介紹了斐波那契數列的性質、斐波那契數列在音樂中的展現、斐波那契螺旋、斐波那契螺旋的構造、二階遞歸順序等，進而講述了廣義斐波那契數列，又介紹了生成函數、比耐公式、兩個連續項的商的極限、卡塔蘭恆等式、凱西尼恆等式、辛普森恆等式等，最後給出了廣義斐波那契數列恆等式的相關內容。