On The Connections Between Jacobsthal Numbers and Fibonacci p-Numbers

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Turkish Journal of Science
Volume:5 Issue:2
On The Connections Between Jacobsthal Numbers and Fibonacci p-Numbers

On The Connections Between Jacobsthal Numbers and Fibonacci p-Numbers

Authors : Özgür ERDAĞ, Ömür DEVECİ

Pages : 147-156

View : 16 | Download : 11

Publication Date : 2020-10-31

Article Type : Research Paper

Abstract :In this paper, we define the Fibonacci-Jacobsthal p-sequence and then we discuss the connection of the Fibonacci-Jacobsthal p-sequence with Jacobsthal and Fibonacci p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of Fibonacci-Jacobsthal p-numbers by the aid of the nth power of the generating matrix the Fibonacci-Jacobsthal p-sequence. Furthermore, we derive relationships between the Fibonacci-Jacobsthal p-numbers and their permanent, determinant and sums of certain matrices.
Keywords : Jacobsthal sequence, Fibonacci p sequence, Matrix, Representation

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