A Class of Recurrent Sequences Exhibiting Some Exciting Properties of Balancing Numbers
The balancing numbers are natural numbers n satisfying
the Diophantine equation 1 + 2 + 3 + · · · + (n - 1) = (n + 1) +
(n + 2) + · · · + (n + r); r is the balancer corresponding to the
balancing number n.The nth balancing number is denoted by Bn
and the sequence {Bn}1
n=1 satisfies the recurrence relation Bn+1 =
6Bn-Bn-1. The balancing numbers posses some curious properties,
some like Fibonacci numbers and some others are more interesting.
This paper is a study of recurrent sequence {xn}1
n=1 satisfying the
recurrence relation xn+1 = Axn - Bxn-1 and possessing some
curious properties like the balancing numbers.
[1] Behera A. and Panda G.K., On the square roots of triangular numbers,
The Fibonacci Quaterly, 37(2) (1999), 98-105.
[2] Panda G.K., Some fascinating properties of balancing numbers, Applications
of Fibonacci Numbers,Congressus Numerantium, Vol 194, 185-190,
2006.
[3] Panda G.K. and Ray P.K., Cobalancing numbers and cobalancers,
International Journal of mathematics and Mathematical
Sciences,(8)(2005),1189-1200.
[4] Niven I. and Zuckerman H.L., An Introduction to the theory of Numbers,
Wiley Eastern Limited, New Delhi 1991.
[1] Behera A. and Panda G.K., On the square roots of triangular numbers,
The Fibonacci Quaterly, 37(2) (1999), 98-105.
[2] Panda G.K., Some fascinating properties of balancing numbers, Applications
of Fibonacci Numbers,Congressus Numerantium, Vol 194, 185-190,
2006.
[3] Panda G.K. and Ray P.K., Cobalancing numbers and cobalancers,
International Journal of mathematics and Mathematical
Sciences,(8)(2005),1189-1200.
[4] Niven I. and Zuckerman H.L., An Introduction to the theory of Numbers,
Wiley Eastern Limited, New Delhi 1991.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:60828", author = "G.K.Panda and S.S.Rout", title = "A Class of Recurrent Sequences Exhibiting Some Exciting Properties of Balancing Numbers", abstract = "The balancing numbers are natural numbers n satisfying
the Diophantine equation 1 + 2 + 3 + · · · + (n - 1) = (n + 1) +
(n + 2) + · · · + (n + r); r is the balancer corresponding to the
balancing number n.The nth balancing number is denoted by Bn
and the sequence {Bn}1
n=1 satisfies the recurrence relation Bn+1 =
6Bn-Bn-1. The balancing numbers posses some curious properties,
some like Fibonacci numbers and some others are more interesting.
This paper is a study of recurrent sequence {xn}1
n=1 satisfying the
recurrence relation xn+1 = Axn - Bxn-1 and possessing some
curious properties like the balancing numbers.", keywords = "Recurrent sequences, Balancing numbers, Lucas balancing
numbers, Binet form.", volume = "6", number = "1", pages = "79-3", }