Geodesic
Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 229-237

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The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation. This recurrence relation can be extended to generalized quaternion algebras. Also, the fourth order recurrence relation has application in coding theory.
Keywords: balancing numbers, Lucas-balancing numbers, quaternion algebra, Coding theory, Pell and Lucas-Pell numbers 
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Patra, Asim. Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 229-237. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a1/