WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
On One-Parameter Generalization of Jacobsthal Numbers
Authors: ,
Abstract: In this paper, we discuss a one-parameter generalization of Jacobsthal numbers that preserves the
recurrence relation with arbitrary initial conditions. We introduce generalized Jacobsthal-Lucas-like numbers,
which are simple associations of generalized Jacobsthal numbers. Consequently, we give some new and
well-known identities. Furthermore, we propose integral representations of these numbers associated with
generalized Jacobsthal and Jacobsthal-Lucas-like numbers. Our results not only generalize the integral
representations of the Jacobsthal and Jacobsthal-Lucas numbers but also apply to all one-parameter generalizations
of Jacobsthal numbers.
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Keywords: one-parameter Jacobsthal number, generalized Jacobsthal number, generalized Jacobsthal-Lucas
number, generalized Jacobsthal-Lucas-like number, Jacobsthal number, Jacobsthal-Lucas number, integral
representation.
Pages: 51-61
DOI: 10.37394/23206.2025.24.7