• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.473-486
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• 2021

We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.539-550
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• 2023

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.