A Trigonometry Approach to Balancing Numbers and Their Related Sequences

Authors

  • Prasanta Kumar Ray IIIT BhubaneswarIndia

Keywords:

Triangular numbers, Balancing numbers, Lucas-balancing numbers, Cobalancing numbers, Recurrence relation

Abstract

The balancing numbers satisfy the second order linear homogeneous dierence equation Bn+1 = 6Bn - Bn-1, on the other hand the Fibonacci numbers are solution of the second order linear homogeneous dierence equation Fn+1 = Fn + Fn-1; where Bn and Fn denote the nth balancing number and nth Fibonacci number respectively. In a paper, Smith introduce Fibonometry in connection with a dierential equation called Fibonometric dierential equation. In this study, we first introduce the balancometric dierential equation and then obtain the balancometric functions as solutions of this equation.

Author Biography

Prasanta Kumar Ray, IIIT BhubaneswarIndia

Mathematics

Assistant Professor

References

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Published

21-08-2017

How to Cite

Ray, P. K. (2017). A Trigonometry Approach to Balancing Numbers and Their Related Sequences. Sigmae, 5(2), 1–7. Retrieved from https://publicacoes.unifal-mg.edu.br/revistas/index.php/sigmae/article/view/323

Issue

Section

Pure Mathematics