Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Generalized k-Balancing and k-Lucas Balancing Numbers and Associated Polynomials

  • Kalika Prasad (Department of Mathematics, Central University of Jharkhand) ;
  • Munesh Kumari (Department of Mathematics, Central University of Jharkhand) ;
  • Jagmohan Tanti (Department of Mathematics, Babasaheb Bhimrao Ambedkar University)
  • Received : 2023.02.07
  • Accepted : 2023.08.09
  • Published : 2023.12.31
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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.

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References

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