Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras

Abstract

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
• 11b37
• 11b39
• 11d09