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)**

## Details

### 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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## Cite this paper

Frontczak, R. (2019). Identities for generalized balancing numbers. *Notes on Number Theory and Discrete Mathematics*, 25(2), 169-180, DOI: 10.7546/nntdm.2019.25.2.169-180.