A Class of Recurrent Sequences Exhibiting Some Exciting Properties of Balancing Numbers
نویسندگان
چکیده
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 n balancing number is denoted by Bn and the sequence {Bn} ∞ 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} ∞ 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.
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