The generalized k-sequence

Abstract

A new notion, called generalized k-sequence, which is a sequence satisfying a second order linear recurrence with coefficients depending on two independent parameters, is introduced. The set of such sequences contains almost all previously known extensions of the Fibonacci and Lucas sequences. Properties of the generalized k-sequence are derived, and a new coding-decoding method arising from such sequences is developed.

Subject Classification:

• 11B37
• 11B39
• 90B35
• 11T71

Keywords:

• k-sequence
• Fibonacci numbers
• Lucas numbers
• Fibonacci coding
• code matrix