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On the Fibonacci k-numbers
We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers {Fk,n}n=0∞ were found byExpand
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The k-Fibonacci sequence and the Pascal 2-triangle
The general k-Fibonacci sequence {Fk,n}n=0∞ were found by studying the recursive application of two geometrical transformations used in the well-known 4-triangle longest-edge (4TLE) partition. ThisExpand
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On the k-Lucas Numbers
From a special sequence of squares of k-Fibonacci numbers, the kLucas sequences are obtained in a natural form. Then, we will study the properties of the k-Lucas numbers and will prove theseExpand
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On k-Fibonacci sequences and polynomials and their derivatives
The k-Fibonacci polynomials are the natural extension of the k-Fibonacci numbers and many of their properties admit a straightforward proof. Here in particular, we present the derivatives of theseExpand
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On k-Fibonacci numbers of arithmetic indexes
TLDR
In this paper, we study the sums of k-Fibonacci numbers with indexes in an arithmetic sequence, say an þ r for fixed integers a and r. Expand
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On the complex k-Fibonacci numbers
We first study the relationship between the k-Fibonacci numbers and the elements of a subset of . Later, and since generally studies that are made on the Fibonacci sequences consider that theseExpand
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Mesh quality improvement and other properties in the four-triangles longest-edge partition
TLDR
The four-triangles longest-edge partition of a triangle t is obtained by joining the midpoint of the longest edge of t to the opposite vertex and to the midpoints of the two remaining edges. Expand
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The k–Fibonacci difference sequences
Abstract In this paper we apply the concept of difference relation to the sequences of k –Fibonacci numbers. We will obtain general formulas to find any term of the ith k –Fibonacci differenceExpand
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Binomial Transforms of the k-Fibonacci Sequence
In this paper, we apply the binomial, k-binomial, rising, and falling transforms to the k-Fibonacci sequence. Many formulas relating the so obtained new sequences are presented and proved. Finally,Expand
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On the k-Lucas Numbers of Arithmetic Indexes
In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularlyExpand
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