2017
DOI: 10.17512/jamcm.2017.2.13
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Fibonacci-Like sequence associated with k-Pell, k-Pell-Lucas and Modified k-Pell sequences

Abstract: Abstract. Fibonacci sequence is a well known example of second order linear recurrence relatio. Besides Fibonacci numbers and their generalizations have many applications as well as interesting properties almost in every field of science such as in Physics, Biology, Mathematics (Algebra, Geometry and Number Theory itself). The main aim of the present article to introduce a generalization of Fibonacci sequence which is similar to k-Pell, k-Pell-Lucas, Modified k-Pell sequences and known as Fibonacci-Like sequen… Show more

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“…with R k,0 = 2 and R k,1 = 1 ( [15]). Clearly x 2 − 2x − k = 0 is also the characteristic equation of R k,n = 2R k,n−1 + kR k,n−2 recurrence formula in equation 5and a and b are its two roots where a = 1 + √ 1 + k and b = 1 − √ 1 + k. Many properties of these number sequences are deduced directly from elementary matrix algebra.…”
Section: Introductionmentioning
confidence: 99%
“…with R k,0 = 2 and R k,1 = 1 ( [15]). Clearly x 2 − 2x − k = 0 is also the characteristic equation of R k,n = 2R k,n−1 + kR k,n−2 recurrence formula in equation 5and a and b are its two roots where a = 1 + √ 1 + k and b = 1 − √ 1 + k. Many properties of these number sequences are deduced directly from elementary matrix algebra.…”
Section: Introductionmentioning
confidence: 99%