Refine your search
Collections
Co-Authors
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Davala, R. K.
- On Sum and Ratio Formulas for Balancing Numbers
Abstract Views :218 |
PDF Views:2
Authors
R. K. Davala
1,
G. K. Panda
1
Affiliations
1 Department of Mathematics, National Institute of Technology, Rourkela-769 008, IN
1 Department of Mathematics, National Institute of Technology, Rourkela-769 008, IN
Source
The Journal of the Indian Mathematical Society, Vol 82, No 1-2 (2015), Pagination: 23-32Abstract
This paper deals with the construction of explicit formulas for sum of consecutive balancing numbers, consecutive even/odd balancing numbers, squares of consecutive balancing numbers, squares of consecutive even/odd balancing numbers and pronic product of balancing numbers. Sums of these numbers with alternative signs give beautiful results. When indices are in arithmetic progression, ratios of sums and differences follow certain interesting patterns.Keywords
Balancing and Lucas Balancing Numbers, Balancer, Integer Sequences, Binet Form.- Shift Balancing Numbers
Abstract Views :264 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, National Institute of Technology, Rourkela - 769 008, IN
2 Department of Mathematics, Gayatri Vidya Parishad College of Engineering (A), Visakhapatnam - 530048, IN
1 Department of Mathematics, National Institute of Technology, Rourkela - 769 008, IN
2 Department of Mathematics, Gayatri Vidya Parishad College of Engineering (A), Visakhapatnam - 530048, IN
Source
The Journal of the Indian Mathematical Society, Vol 87, No 1-2 (2020), Pagination: 131–136Abstract
For each positive integer k, the Diophantine equation (k+1)+(k+2)+···+(n−1) = (n+1)+(n+2)+···+(n+r) is studiedKeywords
Lancing Numbers, Lucas-Balancing Numbers, Gap Balancing Numbers, t−balancing Numbers.References
- A. Behera and G. K. Panda, On the square ischolar_mains of triangular numbers, Fibonacci Quart., 37(2) (1999), 98-105.
- K. K. Dash and R. S. Ota, t−Balancing Numbers, Int. J. Contemp. Math. Sciences, 7 (2012), 1999- 2012.
- R. K. Davala and G. K. Panda, On sum and ratio formulas for balancing numbers, J. Ind. Math. Soc., 82(1-2) (2015), 23-32.
- R. P. Finkelstein, The House Problem, Amer. Math. Monthly, 72 (1965), 1082-1088.
- T. Kovács, K. Liptai and P. Olajos, On (a,b)-balancing numbers, Publ. Math. Debrecen, 77(3) (2010).
- K. Liptai, Fibonacci Balancing Numbers, Fibonacci Quart., 42(4) (2004), 330-340.
- K. Liptai, Lucas balancing numbers, Commun. Math., 14(1) (2006), 43-47.
- R. A. Mollin, Fundamental number theory with applications, Boca Raton, CRC press, London (2004).
- G. K. Panda and R. K. Davala, Perfect balancing numbers, Fibonacci Quart., 53(3) (2015), 261-264.
- G. K. Panda and P. K. Ray, Cobalancing numbers and cobalancers, Internat. J. Math. Math. Sci., 8 (2005), 1189-1200.
- G. K. Panda, Some fascinating properties of balancing numbers, In Proc. of Eleventh Internat. Conference on Fibonacci Numbers and Their Applications, Cong. Numerantium, 194, (2009), 185-189.
- G. K. Panda and A. K. Panda, Almost balancing numbers, J. Ind. Math. Soc., 82(3-4) (2015), 147-156.
- G. K. Panda and S. S. Rout, Periodicity of balancing numbers, Acta. Math. Hungar., 143(2) (2014), 274-286.
- S. S. Rout and G. K. Panda, k-gap balancing numbers, Mathematika, 70(1) (2015), 109-121.
- S. S. Rout, R. K. Davala and G. K. Panda, Stability of balancing sequence modulo p, Unif. Distrib. Theory, 10(2) (2015), 77-91.