Generalized a:k:m-Fibonacci Numbers
Asian Research Journal of Mathematics · pp. 1–12 · Published 27 Aug 2018
10.9734/ARJOM/2018/42751Abstract
The a:k:m-Fibonacci sequence is defined recursively by . We introduce the generalized a:k:m-Fibonacci sequence with arbitrary integers and and study some important properties relating to the Pascal type triangle generated from this sequence. The results are extended to negative values of and , an important concept which brings on board Lehmer type sequences. Most importantly, generalized a:k:m-Fibonacci sequences provide a means to unify ideas that are otherwise treated independently. The theory of a:k:m-Fibonacci numbers is therefore a unification theory
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