Generalized k-Balancing and k-Lucas Balancing Numbers and Associated Polynomials
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In this paper, we define the generalized k-balancing numbers {B(k)n } and k Lucas balancing numbers {C(k)n } and associated polynomials, where n is of the form sk+r, 0 ≤ r < k. We give several formulas for these new sequences in terms of classic balancing and Lucas balancing numbers and study their properties. Moreover, we give a Binet style formula, Cassini’s identity, and binomial sums of these sequences.
Abstract
In this paper, we define the generalized k-balancing numbers {B(k)n } and k Lucas balancing numbers {C(k)n } and associated polynomials, where n is of the form sk+r, 0 ≤ r < k. We give several formulas for these new sequences in terms of classic balancing and Lucas balancing numbers and study their properties. Moreover, we give a Binet style formula, Cassini’s identity, and binomial sums of these sequences.
참고문헌 (13)
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