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On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers
Version 1
: Received: 11 June 2019 / Approved: 13 June 2019 / Online: 13 June 2019 (06:22:28 CEST)
How to cite: Soykan, Y. On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers. Preprints 2019, 2019060110. https://doi.org/10.20944/preprints201906.0110.v1 Soykan, Y. On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers. Preprints 2019, 2019060110. https://doi.org/10.20944/preprints201906.0110.v1
Abstract
In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.
Keywords
Pentanacci numbers; Gaussian generalized Pentanacci numbers; Gaussian Pentanacci numbers; Gaussian Pentanacci-Lucas numbers
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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