On a two-parameter generalization of Jacobsthal numbers and its graph interpretation

Dorota Bród

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.

Keywords


Jacobsthal numbers; generalized Jacobsthal numbers; Binet’s formula; generating function; graph interpretation; Merrifield-Simmons index

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References


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DOI: http://dx.doi.org/10.17951/a.2018.72.2.21
Data publikacji: 2018-12-22 22:03:11
Data złożenia artykułu: 2018-12-21 22:00:43


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