- Turkish Journal of Science
- Vol: 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 Deveci
Pages : 147-156
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Publication Date : 2020-10-31
Article Type : Research
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