Abstract
The main scenario of this paper is to introduce a new sequence of Jacobsthal type having a generalized orderj. Some basic properties will be studied concerning it. Also, we will establish the generalized Binet formula.
Highlights
Background and IntroductionThe Fibonacci sequence is an integer sequence plays a vital role for many fascinating identities
Choosing s = 0, the sequence wrn gets reduced to the generalized order-j Fibonacci sequence [25]
This part of the article deals with the derivation of Generalized Binet Formula (GBF) for generalized order j-Jacobsthal numbers
Summary
Background and IntroductionThe Fibonacci sequence is an integer sequence plays a vital role for many fascinating identities. The authors in [16, 17] have defined the Jacobsthal numbers Jn by the following recurrence relation: J0 = 0, J1 = 1, Jn+2 = Jn+1 + 2Jn, n ≥ 0: ð1Þ In [15], the authors have studied Jacobsthal F-matrix as follows: For n > 0 and 1 ≤ r ≤ j, the authors in [19] have defined the j sequences of the generalized order jJacobsthal numbers as follows: J
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