本书共包含十三章内容，介绍了数学研究者及工程研究者经常遇到或使用的广义斐波那契数列，通过大量的文献证明了斐波那契数的普遍性。本书首先由兔子问题引入，介绍了斐波那契数列的历史背景，然后介绍了斐波那契数列的性质、斐波那契数列在音乐中的展现、斐波那契螺旋、斐波那契螺旋的构造、二阶递归顺序等，进而讲述了广义斐波那契数列，又介绍了生成函数、比耐公式、两个连续项的商的极限、卡塔兰恒等式、凯西尼恒等式、辛普森恒等式等，很后给出了广义斐波那契数列恒等式的相关内容。
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
编辑手记
