Neşe Ömür

Parametrized Fibonacci search method with k-Lucas numbers

Abstract In this paper, we study on Fibonacci search method with k -Lucas numbers by introducing a parameter α which depends on the length of the interval and the function. This parameter ensures that the result we got at the end of the computation is correct. We made more improvement in algorithm which finds the maximum point of a unimodal function. Application of this algorithm gives better results.

Two Variants of the Reciprocal Super Catalan Matrix

In this paper, we define two kinds variants of the super Catalan matrix as well as their q-analoques. We give explicit expressions for LU-decompositions of these matrices and their inverses.

SOME WEIGHTED SUMS OF PRODUCTS OF LUCAS SEQUENCES

In this paper, we consider the weighted sums of products of Lucas sequences of the form n ∑ k=0 ( n k ) rmksm(tn+k), where rn and sn are the terms of Lucas sequences {Un} and {Vn} for some positive integers t and m. By using generating function methods, we compute the weighted sums of products of Lucas sequences and show that these sums could be expressed via terms of the Lucas sequences.

On Certain Hessenberg Matrices Related with Linear Recurrences

In this paper, we present the permanents and determinants of some Hessenberg matrices. Also, some special cases for permanents are given.

ON THE MATRICES WITH THE GENERALIZED HYPERHARMONIC NUMBERS OF ORDER r

In this paper, we define two n × n matrices An and Bn with ai,j = Hi,jr and bi,j = Hi,mj, respectively, where Hn,mr are a generalized hyperharmonic numbers of order r. We give some new factorizations and determinants of the matrices An and Bn.

Generalized Binomial Convolution of the mth Powers of the Consecutive Integers with the General Fibonacci Sequence

Abstract In this paper, we consider Gauthier’s generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.

A curious matrix-sum identity and certain finite sums identities

In this paper, we consider two generalized binary sequences and then give a generalization of a matrix equality proposed as an advanced problem. Then, we derive new certain finite sums including the generalized binary sequences as applications.

A New Perspective to the Generalization of Sequences of t-Order

K. Atanassov, L. Atanassov, and D. Sasselov (1983), A New Perspective to the Generalization of the Fibonacci Sequence, The Fibonacci Quarterly, Volume 23, Issue 1, Pages:21-28. K. Atanassov, On a second new generalization of the Fibonacci sequence (1986), The Fibonacci Quarterly, Volume 23, Issue 4, Pages:362-365. K. Atanassov, V. Atanassova, A. Shannon and J. Turner (2002), New Visual Perspectives on Fibonacci Numbers, New Jersey. J. Z. Lee and J. S. Lee (1987), Some Properties of the generalization of the Fibonacci

On Reciprocal Series of Generalized Fibonacci Numbers with Subscripts in Arithmetic Progression

We investigate formulas for closely related series of the forms: ∑ ∞ 𝑛 = 0 1 / ( 𝑈 𝑎 𝑛 + 𝑏 + 𝑐 ) , ∑ ∞ 𝑛 = 0 ( − 1 ) 𝑛 𝑈 𝑎 𝑛 + 𝑏 / ( 𝑈 𝑎 𝑛 + 𝑏 + 𝑐 ) 2 , ∑ ∞ 𝑛 = 0 𝑈 2 ( 𝑎 𝑛 + 𝑏 ) / ( 𝑈 2 𝑎 𝑛 + 𝑏 + 𝑐 ) 2 for certain values of 𝑎 , 𝑏 , and 𝑐 .

Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers

By considering Melhams sums (Melham, 2004), we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (−1)2𝑛