New Number Sequences Obtained with Grouping of Fibonacci Numbers

Abstract

Abstract

The relations of the sum and difference of two Fibonacci numbers, in which the difference of subscripts is even, was given by Koshy. In this study, the relations of the sum and difference of two Fibonacci numbers, in which is the difference of subscripts is odd, is introduced by using the generating functions. Similar results are given for Lucas numbers. Also, two new family of Fibonacci numbers are obtained.

Keywords: Binet Formula, Fibonacci sequence, the generalized Fibonacci sequence, Generating functions, Lucas sequence.