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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 these properties will be related with the k-Fibonaci numbers. In this paper we examine some of the interesting properties of the k-Lucas numbers themselves as well as looking at its close relationship with the k-...

This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower (Helianthus annuus) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci and non-Fibonacci structure is informative for challenging such models. We collected data on 657 sunflowers. In our most reliable data subset, w...

In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and p-numbers in the distance sense, using definition a between by recurrence relation according to parameter k. Tiling combinatorial interpretations these are presented, explicit formulas that allow us calculate nth number given. Also, their generating functions obtained sums ...

ABSTRACT Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of ...

In lipid biochemistry, a fundamental question is how the potential number of fatty acids increases with their chain length. Here, we show that it grows according to the famous Fibonacci numbers when cis/trans isomerism is neglected. Since the ratio of two consecutive Fibonacci numbers tends to the Golden section, 1.618, organisms can increase fatty acid variability approximately by that factor ...

In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which call ordered numbers. We determine the properties numbers including relations with Leonardo, Fibonacci, and Lucas Symmetric antisymmetric Fibonacci are used in proofs. attain some well-known identities, Binet formula, generating function for these Finally, provide illustrations identities.

The main purpose of this paper is to define a new regular matrix by using Fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p