Every term in the Fibonacci Sequence can be determined recursively with the help of initial values F 0 = 0, F 1 = 1. Similar is the case with Lucas Sequence. In this paper, we study Generalized Fibonacci-Like sequence {D n } defined by the recurrence relation D n = D n-1 + D n-2 , for all n  2 with D 0 = 2 and D 1 = 1+m, m being a fixed positive integer. The associated initial conditions are the sum of m times the initial conditions of Fibonacci sequence and the initial conditions of Lucas sequence respectively. We shall define Binet's formula and generating function of Generalized Fibonacci-Like sequence. Mainly, Induction method 236 Sanjay Harne, Bijendra Singh and Shubhraj Pal and Binet's formula will be used to establish properties of Generalized Fibonacci-Like sequence.

In this paper we will prove some generalized identities involving k-Fibonacci sequences and Fibonacci polynomials.

In this paper we prove some identities involving Chebyshev polynomials, Fibonacci and Lucas numbers.

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In this paper we consider Fibonacci inequalities and relate them through the sequence