On sum and ratio formulas for balancing-like sequences

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
Full paper (PDF, 359 Kb)

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

1. Davala, R. K & Panda, G. K. (2015) On sum and ratio formulas for balancing numbers, J. Indian Math. Soc., 82(2), 23–32.
2. Good, I. J. (1974) A reciprocal series of Fibonacci numbers, Fib. Quart., 12(4), 346.
3. Melham, R. S. (1999) Sums of certain products of Fibonacci and Lucas numbers, Fib. Quart., 37(3), 248-251.
4. Melham, R. S. (2000) Sums of certain products of Fibonacci and Lucas numbers – Part II, Fib. Quart., 38(1), 3-7.
5. 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.
6. Ray, P. K. (2009) Balancing and cobalancing numbers, Ph.D. Thesis, National Institute of Technology, Rourkela.
7. Rout, S. S. (2015) Some generalizations and properties of balancing numbers, Ph.D. Thesis, National Institute of Technology, Rourkela.