Identities for generalized balancing numbers

Robert Frontczak
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 169-180
DOI: 10.7546/nntdm.2019.25.2.169-180
Full paper (PDF, 190 Kb)

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Authors and affiliations

Robert Frontczak
Landesbank Baden-Wurttemberg
Am Hauptbahnhof 2, 70173 Stuttgart, Germany

Abstract

We study properties of generalized balancing numbers. We start with some basic identities. Thereafter, we focus on connections to generalized Fibonacci numbers. Using generating functions we prove fundamental relations between these two sequences. Many interesting examples involving balancing, Lucas-balancing, Fibonacci, and Lucas numbers are obtained as special cases of our relations.

Keywords

• Generating function
• Balancing number
• Fibonacci number

2010 Mathematics Subject Classification

• 11B37
• 11B39

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