Formulated New Identities of Fibonacci Numbers with James Abacus Diagram

Abstract

This paper focuses on developing a strategy to represent a new Fibonacci identity using James abacus. The idea of a Graphical chain with respect to the beta numbers and abacus was established to count the number of ways to tile a James diagram chain inscribed infinite grid. Then, the idea of chain abacus and beta numbers were used to find new identities of Fibonacci numbers.

Keywords

• james abacus
• beta number
• fibonacci number
• tile
• chain