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
@article{DMGAA_2021_41_2_a1,
author = {Patra, Asim},
title = {Fascinating {Number} {Sequences} from {Fourth} {Order} {Difference} {Equation} {Via} {Quaternion} {Algebras}},
journal = {Discussiones Mathematicae. General Algebra and Applications},
pages = {229--237},
publisher = {mathdoc},
volume = {41},
number = {2},
year = {2021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a1/}
}
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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/