Extending the Theory of k-Fibonacci and k-Lucas Numbers
Lovemore Mamombe *
Independent Researcher, Harare, Zimbabwe.
*Author to whom correspondence should be addressed.
Abstract
The a:k:m-Fibonacci sequences 
and the a:k:m-Lucas sequences 
are introduced. The well-known k-Fibonacci and k-Lucas sequences become a particular case (a=m=1). One might be interested to meet the equally famous Jacobsthal sequence at 2,1. Our brief results capture the most important properties relating to the assemblage mechanics of these sequences.
Keywords: a:k:m-Fibonacci numbers, a:k:m-Lucas numbers, Jacobsthal numbers, k-Fibonacci numbers, k-Lucas numbers, metallic means