Binomial Transform of the Generalized \(k\)-Fibonacci Numbers
Keywords:\(k\)-Fibonacci numbers, Generalization of the \(k\)-Fibonacci numbers, Generating function, Binomial transform
We recall the concept and some properties of the generalized \(k\)-Fibonacci numbers and then apply the binomial transform to these sequences. As consequence, we obtain new integer sequences related to the generalized \(k\)-Fibonacci numbers. Finally, we find the recurrence relation of these new sequences and the formulas for their sums.
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