We say the k-Fibonacci numbers Fk,i and Fk,j are equidistant
if j = n - i and then we study some properties of these pairs of numbers. As a
main result, we look for the formula to find the generating function of the
product of the equidistant numbers, their sums and their binomial transforms.
Next, we apply this formula to some simple cases but more common than the
general cases. In particular, we define the half-self-convolution of the
k-Fibonacci and k-Lucas sequences. Finally, we study the sum of these new
sequences, their recurrence relations, and their generating functions.
Author(s) Details
Sergio Falcon
Department of Mathematics, University of Las Palmas de Gran Canaria, Campus
de Tafira, 35017 - Las Palmas de Gran Canaria, Spain.
Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v1/621
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