Bulunan: 15 Adet 0.001 sn
Konu Başlıkları Padovan numbers
170354

ON THE BICOMPLEX PADOVAN AND BICOMPLEX PERRIN NUMBERS

Dişkaya, Orhan | Menken, Hamza

In this paper we first introduce the bicomplex Padovan and bicom- plex Perrin numbers which generalize Padovan and Perrin numbers, and then we derive the Binet-like formulas, the generating functions and the exponential gen- erating functions, series, sums of these sequences. Also, we obtain some binomial identities for them.

170384

On the bivariate Padovan polynomials matrix

Dişkaya, Orhan | Menken, Hamza

In this paper, we intruduce the bivariate Padovan sequence we examine its various identities. We define the bivariate Padovan polynomials matrix. Then, we find the Binet formula, generating function and exponential generating function of the bivariate Padovan polynomials matrix. Also, we obtain a sum formula and its series representation.

170392

ON THE NOVEL GENERALIZATIONS OF THE PADOVAN SEQUENCE

Dişkaya, Orhan | Menken, Hamza

In the present work, we consider the Padovan sequence and define a sequence (called Quadrovan) that is a new generalization. In addition, we give the previously defined Tridovan sequence as a generalization of the Padovan sequence. We derive the Binet-like formulas, the generating functions and the exponential generating functions for the Tridovan and Quadrovan sequences. Also, we establish their series and matrices.

170402

ON THE PADOVAN ARRAYS

Dişkaya, Orhan | Menken, Hamza

In the present work, two new recurrences of the Padovan sequence given with delayed initial conditions are defined. Some identities of these sequences which we call the Padovan arrays were examined. Also, generating and series functions of the Padovan arrays are examined.

170404

On the Richard and Raoul numbers

Dişkaya, Orhan | Menken, Hamza

In this study, we define and examine the Richard and Raoul sequences and we deal with, in detail, two special cases, namely, Richard and Raoul sequences. We indicate that there are close relations between Richard and Raoul numbers and Padovan and Perrin numbers. Moreover, we present the Binet-like formulas, generating functions, summation formulas, and some identities for these sequences.

170470

SOME IDENTITIES OF GADOVAN NUMBERS

Dişkaya, Orhan | Menken, Hamza

In this parer, we consider Padovan numbers with different initial values. We define the Gadovan numbers which generalizes a new class of Padovan numbers, and we derive Binet-like formulas, generating functions, exponential generating functions for the Gadovan numbers. Also, we obtain binomial sums, some identities and a matrix of the Gadovan numbers.

170398

PADOVAN POLYNOMIALS MATRIX

Dişkaya, Orhan | Menken, Hamza

In this paper, we explore the Padovan numbers and polynomials, and define the Padovan polynomials matrix. We obtain its Binet-like formula and a sum formula. Subsequently, we derive the Padovan polynomials matrix series. Additionally, we establish the generating and exponential generating functions for the Padovan polynomials matrix.

170397

ON THE WEIGHTED PADOVAN AND PERRIN SUMS

Dişkaya, Orhan | Menken, Hamza

In this paper, we obtain various weighted sum formulas using several sum formulas of Padovan and Perrin numbers.

170321

PADOVAN AND PERRIN SPINORS

Dişkaya, Orhan | Menken, Hamza

Spinors are components of a complex vector space that can be re- lated to Euclidean space in both geometry and physics. In essence, the forms of usage include quaternions that are equivalent to Pauli spin matrices, which may be produced by thinking of a quaternion matrix as the compound. This study’s objective is the spinor structure that forms based on the quaternion al- gebra. In this work, first, spinors have been mathematically presented. Then, Padovan and Perrin spinors have been defined using the Padovan and Perrin quaternions. Later, we defined the algebraic structure for these spinors. Fi- nally, we have established certain identities such as the Binet formulas and generating functions for Padovan and Perrin spinors.

Makale2024MAT-KOL (Banja Luka) 6 | 0 Erişime Açık
170472

ON THE (s, t)-PADOVAN AND (s, t)-PERRIN QUATERNIONS

Dişkaya, Orhan | Menken, Hamza

In this paper we first introduce a class of (s, t)-Padovan and (s, t)-Perrin quaternions which generalizes Padovan and Perrin quaternions, and then we derive new Binet-like formulas, generating functions and certain binomial sums for these quaternions.

Makale2019J. Adv. Math. Stud. 2 | 0 Erişime Kapalı
170352

Compositions of positive integers with 2s and 3s

Dişkaya, Orhan | Menken, Hamza

In this article, we consider compositions of positive integers with 2s and 3s. We see that these compositions lead us to results that involve Padovan numbers, and we give some tiling models of these composi- tions. Moreover, we examine some tiling models of the compositions related to the Padovan polynomials and prove some identities using the tiling model’s method. Next, we obtain various identities of the compositions of positive integers with 2s and 3s related to the Padovan numbers. The number of palindromic compositions of this type is determined, and some numerical arithmetic functions are defined. Finally, we provide a table that compares all of the results obtained from compositions of positive integers with 2s and 3s.

Makale2023Demonstratio Mathematica 12 | 0 Erişime Açık
167127

On the Non-Newtonian Padovan and Non-Newtonian Perrin Numbers

Dişkaya, Orhan

In this work, we introduce a novel version of Padovan and Perrin numbers which we refer to as non-Newtonian Padovan and non-Newtonian Perrin numbers. Furthermore, we examine about a number of their properties. Additionally, we provide a variety of identities and formulas involving these new kinds, including the Binet-like formulas, the generating functions, the partial sum formulas, and the binomial sum formulas.

170288

ON THE QUATERNION PADOVAN NUMBERS

Dişkaya, Orhan | Menken, Hamza

In this paper, we define the quaternion Padovan sequence. We obtain some identities for this quaternion sequence. Also, we derive a plastic-like ratio.

170475

On the Split (s, t)-Padovan and (s, t)-Perrin Quaternions

Dişkaya, Orhan | Menken, Hamza

In this paper we consider the generalization of Padovan and Perrin quaternions. We define the split (s, t)-Padovan and (s, t)- Perrin quaternions which generalize Padovan and Perrin quaternions. We derive the Binet-like formulas for the split (s, t)-Padovan and (s, t)-Perrin quaternions. We establish their generating functions. Also, we obtain certain binomial sums regarding the split (s, t)- Padovan and (s, t)-Perrin quaternions.

170467

On the Padovan Triangle

Dişkaya, Orhan | Menken, Hamza

In the present work, we consider the Padovan numbers. Inspiring of the Hosoya’s triangle, we define the Padovan triangle. We give some identities and properties of the Padovan triangle.