Takao Komatsu

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 2, Pages 71—84

DOI: 10.7546/nntdm.2020.26.2.71-84

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## Details

### Authors and affiliations

Takao Komatsu

*Department of Mathematics, School of Science, Zhejiang Sci-Tech University
Hangzhou 310018 China
*

### Abstract

Let be the -th balancing number. In this paper, we give some explicit expressions of and . We also consider the convolution identities with binomial coefficients:.This type can be generalized, so that is a special case of the number , where () with and .

### Keywords

- Convolutions
- Balancing numbers

### 2010 Mathematics Subject Classification

- Primary 11B39
- Secondary 11B83, 05A15, 05A19

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## Related papers

- Prodinger, H. (2021). How to sum powers of balancing numbers efficiently. Notes on Number Theory and Discrete Mathematics, 27(1), 134-137.

## Cite this paper

Komatsu, T. (2020). Higher-order identities for balancing numbers. Notes on Number Theory and Discrete Mathematics, 26 (2), 71-84, doi: 10.7546/nntdm.2020.26.2.71-84.