Preprint Article Version 1 This version is not peer-reviewed

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 (doi: 10.20944/preprints201906.0110.v1). Soykan, Y. On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers. Preprints 2019, 2019060110 (doi: 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.

Subject Areas

Pentanacci numbers; Gaussian generalized Pentanacci numbers; Gaussian Pentanacci numbers; Gaussian Pentanacci-Lucas numbers

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