A New Generalization for Jacobsthal and Jacobsthal Lucas Sequences

S. Uygun

Abstract


In this study, we define\textit{\ new generalizations for }Jacobsthal and Jacobsthal Lucas \textit{sequences called }$p(x)-$Jacobsthal and $p(x)-$% Jacobsthal \textit{Lucas polynomial sequences where }$p(x)$ \textit{is any real valued polynomial. We get the Binet formulae, generating functions, and some important properties for these sequences. And then we describe a matrix whose elements are of }$p(x)-$Jacobsthal\textit{\ terms. By using this matrix we derive some properties for }$p(x)-$Jacobsthal and $p(x)-$% Jacobsthal \textit{Lucas polynomial sequences}

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