Binomial Transform of the Generalized \(k\)-Fibonacci Numbers - Falcón, Sergio (Communications in Mathematics and Applications, 2019)
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.