Cobalancing Numbers: Another Way of Demonstrating Their Properties
Abstract
In this study, previously obtained cobalancing numbers are considered from a different perspective, and the properties of the numbers are re-examined. The main purpose is to change the recurrence relation of cobalancing numbers and calculate some relations and properties in a more diverse and easier way. The reason that led us to this method is that the recurrence relation of cobalancing numbers has a second-order but non-homogeneous difference equations. Thus, it will be much easier to find the Binet formula, generating function, sum formulas, and many other relations with a sequence that is homogeneous and has a third-degree recurrence relation. Also some identities that have not been found before in the sequence are also included in this study.
Keywords
Binet formulas, Cobalancing numbers, Third-order recurrence relations
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