**Ravi Kumar Davala and G. K. Panda**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 22, 2016, Number 3, Pages 45—53

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## Details

### Authors and affiliations

Ravi Kumar Davala

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

G. K. Panda

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

### Abstract

Certain sum formulas with terms from balancing-like and Lucas-balancing-like sequences are discussed. The resemblance of some of these formulas with corresponding sum formulas involving natural numbers are exhibited.

### Keywords

- Balancing-like sequences
- Lucas-balancing-like sequences
- Fibonacci sequence
- Binet form

### AMS Classification

- 11B39

### References

- Davala, R. K & Panda, G. K. (2015) On sum and ratio formulas for balancing numbers, J. Indian Math. Soc., 82(2), 23–32.
- Good, I. J. (1974) A reciprocal series of Fibonacci numbers, Fib. Quart., 12(4), 346.
- Melham, R. S. (1999) Sums of certain products of Fibonacci and Lucas numbers, Fib. Quart., 37(3), 248-251.
- Melham, R. S. (2000) Sums of certain products of Fibonacci and Lucas numbers – Part II, Fib. Quart., 38(1), 3-7.
- Panda, G. K. & Rout, S. S. (2012) A class of recurrent sequences exhibiting some exciting properties of balancing numbers, Int. J. Math. Comp. Sci., 6, 4–6.
- Ray, P. K. (2009) Balancing and cobalancing numbers, Ph.D. Thesis, National Institute of Technology, Rourkela.
- Rout, S. S. (2015) Some generalizations and properties of balancing numbers, Ph.D. Thesis, National Institute of Technology, Rourkela.

## Related papers

## Cite this paper

APAKumar Davala, R., & Panda, G. K. (2016). On sum and ratio formulas for balancing-like sequences, Notes on Number Theory and Discrete Mathematics, 22(3), 45-53.

ChicagoKumar Davala, Ravi and G. K. Panda “On Sum and Ratio Formulas for Balancing-like Sequences.” Notes on Number Theory and Discrete Mathematics 22, no. 3 (2016): 45-53.

MLAKumar Davala, Ravi and G. K. Panda “On Sum and Ratio Formulas for Balancing-like Sequences.” Notes on Number Theory and Discrete Mathematics 22.3 (2016): 45-53. Print.