Geodesic
On Balancing Quaternions and Lucas-Balancing Quaternions
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 55-68

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In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have been obtained for these quaternions.
Keywords: balancing number, Lucas-balancing number, quaternion, Binet formula, generating function 
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Bród, Dorota. On Balancing Quaternions and Lucas-Balancing Quaternions. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 55-68. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a5/