Generalization of Fibonacci Sequence

Fibonacci sequence is one of the most rapidly growing areas of mathematics which has a wide variety of applications in science and mathematics. This sequence is constructed by choosing the first two numbers (The "seeds" of the sequence) then assigning the rest by the rule that each number be the sum of the two preceding numbers. The Fibonacci sequence is defined as 1 1 2 3 5 8 13 21 34 55 89 144 .... The terms are called Fibonacci numbers. Fibonacci numbers are studied as part of number theory and have many applications in the counting of mathematical objects such as sets, permutations and sequences and to computer science. This sequence is a very intriguing and interesting subject. This book is centered on generalization of Fibonacci sequences. Fibonacci sequence has been generalized in a number of ways. The author simply presented the subject matter in his own style and makes the subject easier by giving concepts and number of results related to each chapter. Emphasis has been made on methods of generalization for Fibonacci sequence in various patterns. Identities of coupled Fibonacci sequences are presented in additive and multiplicative forms.