© Science and Education Publishing DOI:10.12691/tjant-2-6-9 Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences

Abstract The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula n n-1 n-2,F F F n 2 = + ≥ and 0 1F 0,F 1 = = , where nF is a n th number of sequence. Many authors have been defined Fibonacci pattern based sequences which are popularized and known as Fibonacci-Like sequences. In this paper, Generalized Fibonacci-Like sequence is introduced and defined by the recurrence relation 1 2n n nB B B − − = +, 2n ≥ with 0 1B 2,B 1s s = = +, where s being a fixed integers. Some identities of Generalized Fibonacci-Like sequence associated with Fibonacci and Lucas sequences are presented by Binet’s formula. Also some determinant identities are discussed