A Note On The Generalizations of Jacobthal and Jacobthal-Lucas Sequences

Abstract

In this paper, we present the generalization of Jacobsthal and Jacobsthal-Lucas sequences by the recurrence relations,,,,,,,,,,,,,,,,, with the initial conditions,,,,,,,,,,,,,,,,,,,,,, . We establish some of the interesting properties of involving them. Also we describe and derive sums, connection formulae and Generating function. We have used their Binet’s formula to derive the identities.

Keywords

• Generalized Jacobsthal sequence,Generalized Jacobsthal-Lucas sequence,Binet’s formula,Generating function

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