Research Article Matrix Structure of Jacobsthal Numbers Abdul Hamid Ganie 1 and Mashael M. AlBaidani 2 1 Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Abha 61421, Saudi Arabia 2 Department of Mathematics, College of Science and Humanities Studies, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi Arabia Correspondence should be addressed to Abdul Hamid Ganie; a.ganie@seu.edu.sa Received 12 June 2021; Revised 12 July 2021; Accepted 28 July 2021; Published 12 August 2021 Academic Editor: Wilfredo Urbina Copyright © 2021 Abdul Hamid Ganie and Mashael M. AlBaidani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The main scenario of this paper is to introduce a new sequence of Jacobsthal type having a generalized order j. Some basic properties will be studied concerning it. Also, we will establish the generalized Binet formula. 1. Background and Introduction The Fibonacci sequence is an integer sequence plays a vital role for many fascinating identities. In nature, it shows its presence, even if certain fruits are looked at, the number of little bumps around each ring is counted or the sand on the beach, and how waves hit it is watched out, the Fibonacci sequence is seen there. It was studied by many authors in the well-known systematic manner, and attrac- tive investigations have been witnessed as can be seen in [1–4]. Further, several recurrence sequences of natural numbers have been object of study for many researchers. Illustrations of these are the Fibonacci, Lucas, Pell, Pell- Lucas, Modified Pell, Jacobsthal, and Jacobsthal-Lucas sequences among others as can be seen in [5–12]. It is well known that the Jacobsthal numbers obey attracting structure in many fields of science, engineering and technology as can be seen in [13–15] and many others. The authors in [16, 17] have defined the Jacobsthal numbers J n by the following recurrence relation: J 0 = 0, J 1 = 1, J n+2 = J n+1 +2 J n , n ≥ 0: ð1Þ The author in [18] has shown that some interesting properties of Fibonacci sequence can be obtained from a matrix description. For a jth Fibonacci number v j , he proved that for A = 0 1 1 1  ! ð2Þ that A n 0 1 ! = v n v n+1 ! : ð3Þ It is obvious that the Jacobsthal sequence is a particu- lar demonstration of a sequence given recursively as fol- lows: a r+j = c 0 a r + c 1 a r+1 +⋯+c j−1 a r+j−1 , ð4Þ where c 0 , c 1 , ⋯, c j−1 are real constants. The author in [10] has determined a closed-form formula for the generalized Hindawi Journal of Function Spaces Volume 2021, Article ID 2888840, 5 pages https://doi.org/10.1155/2021/2888840