**S. G. Rayaguru and G. K. Panda**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 3, Pages 135–148

DOI: 10.7546/nntdm.2020.26.3.135-148

**Full paper (PDF, 324 Kb)**

## Details

### Authors and affiliations

S. G. Rayaguru

*Department of Mathematics, National Institute of Technology
Rourkela, India
*

G. K. Panda

*Department of Mathematics, National Institute of Technology
Rourkela, India
*

### Abstract

A generalization of almost balancing numbers is studied using triangular numbers as the difference between the left and right hand sides of the defining equation of balancing numbers. In case of almost balancing numbers, this difference is kept 1; which is the first triangular number. Some specific representations of these numbers in terms of balancing and balancing related numbers are established and few more results with triangular, square triangular, balancing and balancing related numbers are also studied so as to generalize the identities obtained by A. Tekcan.

### Keywords

- Balancing numbers
- Cobalancing numbers
- Almost balancing numbers
- Lucas-balancing numbers
- Lucas-cobalancing numbers
- Triangular numbers

### 2010 Mathematics Subject Classification

- 11B39
- 11B38

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## Related papers

- Tekcan, A. (2019). Almost balancing, triangular and square triangular numbers,
*Notes on Number Theory and Discrete Mathematics*, 25 (1), 108–121. - Tekcan, A., & Türkmen, E. Z. (2023). Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers.
*Notes on Number Theory and Discrete Mathematics*, 29(4), 682-694.

## Cite this paper

Rayaguru, S. G. & Panda, G. K. (2020). A generalization to almost balancing and cobalancing numbers using triangular numbers. *Notes on Number Theory and Discrete Mathematics*, 26 (3), 135-148, DOI: 10.7546/nntdm.2020.26.3.135-148.