Asian Research Journal of Mathematics, 2456-477X,Vol.: 12, Issue.: 1
On the Dual δ − k − Fibonacci Numbers
1Department of Mathematics, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain.
(1) Dr. Xingting Wang, Department of Mathematics, Temple University, Philadelphia, USA.
(1) Mbakiso F. Mothebe, University of Botswana, Botswana.
(2) Grienggrai Rajchakit, Maejo University, Thailand.
(3) Halil Gorgun, Dicle University, Turkey.
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We define two integer sequences that depend on a parameter and that are related to each other by two recurrence relations. Then we find the Binet formula for the terms of these sequences and, by developing it, we will get an equivalent combinatorial formula. We show that each sequence follows the same relation of recurrence although they differ in the initial conditions. Later we show that these numbers are related to the k − Fibonacci numbers and we finish this section nding its generating functions. Finally, for certain particular values of δ we show that these numbers are related to the Chebyshev polynomials. This paper deals with a new concept of k − Fibonacci sequences linked to each other, so there is no literature on the subject. I hope that this article will be the starting point for other mathematicians that wish to investigate this topic.
k − Fibonacci numbers; k − Lucas numbers; Binomial expansion; geometric sum; generating
function; Chebyshev polynomials.
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DOI : 10.9734/ARJOM/2019/45436Review History Comments