The k-Fibonacci sequence and the Pascal 2-triangle

On sums of odd and even terms of the K-Fibonacci numbers

“…This study has been motivated by the arising of two complex valued maps to represent the two antecedents in an specific four-triangle partition. In [12], Falcon and Plaza k-Fibonacci sequence generalizes, between others, both the classical Fibonacci sequence and the Pell sequence. In this paper many properties of these numbers are deduced and related with the so-called Pascal 2-triangle.…”

On the K-Fibonacci Hankel and the 4 X 4 Skew Symmetric KFibonacci Matrices.

“…For any integer 1 k  , the k-Fibonacci sequence, say   For the properties of the k-Fibonacci numbers, see [3,4].…”

On the generating matrices of the Κ-Fibonacci numbers

“…, we find the following two formulas for the k-Fibonacci numbers according to that n is odd or even [2]:…”

“…We define the k-Fibonacci numbers [1,2,3] by mean of the recurrence relation F k,n+1 = k F k,n + F k,n−1 for n ≥ 1 with the initial conditions F k,0 = 0 and F k,1 = 1.…”