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On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers
This version is not peer-reviewed.
Submitted:
11 June 2019
Posted:
13 June 2019
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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
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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