{"title":"A Class of Recurrent Sequences Exhibiting Some Exciting Properties of Balancing Numbers","authors":"G.K.Panda, S.S.Rout","country":null,"institution":"","volume":61,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":33,"pagesEnd":36,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11795","abstract":"The balancing numbers are natural numbers n satisfying\nthe Diophantine equation 1 + 2 + 3 + \u00b7 \u00b7 \u00b7 + (n - 1) = (n + 1) +\n(n + 2) + \u00b7 \u00b7 \u00b7 + (n + r); r is the balancer corresponding to the\nbalancing number n.The nth balancing number is denoted by Bn\nand the sequence {Bn}1\nn=1 satisfies the recurrence relation Bn+1 =\n6Bn-Bn-1. The balancing numbers posses some curious properties,\nsome like Fibonacci numbers and some others are more interesting.\nThis paper is a study of recurrent sequence {xn}1\nn=1 satisfying the\nrecurrence relation xn+1 = Axn - Bxn-1 and possessing some\ncurious properties like the balancing numbers.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 61, 2012"}