Abstract
The Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, Jacobsthalsequence and Jacobsthal-Lucas sequence are most prominent examples of second order recursivesequences. In this paper, we deal with two companion Fibonacci- Like sequences which aregeneralization of Fibonacci-Like sequence. Further we obtain some generalized identities amongthe terms of companion Fibonacci-Like sequences, Jacobsthal and Jacobsthal-Lucas sequencesthrough Binet’s formulae.
Highlights
It is well known that generalized Fibonacci and Lucas numbers play an important role in many subjects such as algebra, geometry and number theory
We present generalized identities of companion Fibonacci- Like sequences with Jacobsthal and Jacobsthal- Lucas sequences
In this paper we have stated and derived generalized identities of companion Fibonacci-Like sequences with Jacobsthal and Jacobsthal-Lucas sequences
Summary
It is well known that generalized Fibonacci and Lucas numbers play an important role in many subjects such as algebra, geometry and number theory. Their various elegant properties and wide applications have been studied by many authors. The generalization of Fibonacci sequence gives new direction for research. Fibonacci sequence and their generalization have many interesting properties and applications in almost every field of science and art [14] below [14]. In this paper we state and derive generalized identities of companion Fibonacci- Like sequences with Jacobsthal and Jacobsthal- Lucas sequences
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