%0 Journal Article %A G.K.Panda and S.S.Rout %D 2012 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 61, 2012 %T A Class of Recurrent Sequences Exhibiting Some Exciting Properties of Balancing Numbers %U https://publications.waset.org/pdf/11795 %V 61 %X 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. %P 33 - 35