Quaternion-Type Catalan Transforms of the Ï -Fibonacci and Ï -Lucas Numbers

Kübra Gül and Shaofang Hong

Journal of Mathematics, 2023, vol. 2023, 1-11

Abstract: In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties. Then, we introduce a quaternion-type Catalan transform, which is a generalization of the Catalan transform, and its inverse. Moreover, we apply the quaternion-type Catalan transforms to Ï -Fibonacci and Ï -Lucas sequences and derive some new sequences by using these quaternion-type Catalan transforms.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2439110

DOI: 10.1155/2023/2439110

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