Abstract
In this paper we introduce a two-parameter generalization of the classical Jacobsthal numbers ((s,p)-Jacobsthal numbers). We present some properties of the presented sequence, among others Binet’s formula, Cassini’s identity, the generating function. Moreover, we give a graph interpretation of (s,p)-Jacobsthal numbers, related to independence in graphs.
Highlights
The Jacobsthal sequence {Jn} is defined by the second order linear recurrence (1)Jn = Jn−1 + 2Jn−2 for n ≥ 2 with J0 = 0, J1 = 1
In this paper we introduce a new generalization of the classical Jacobsthal numbers
We will describe the terms of the sequence {Jn(s, p)} explicitly by using a generalization of Binet’s formula
Summary
The Binet’s formula of this sequence has the following form Jacobsthal numbers, generalized Jacobsthal numbers, Binet’s formula, generating function, graph interpretation, Merrifield–Simmons index. We define (s, p)-Jacobsthal sequence {Jn(s, p)} by the following recurrence We will describe the terms of the sequence {Jn(s, p)} explicitly by using a generalization of Binet’s formula.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
More From: Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
