Results 21 to 30 of about 1,789,377 (77)
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 We use a new method of matrix decomposition for r‐circulant matrix to get the determinants of An = Circr(F1, F2, …, Fn) and Bn = Circr(L1, L2, …, Ln), where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived.
Jiangming Ma +3 more
wiley +1 more source
Catalan Transform of k‐Balancing Sequences
International Journal of Mathematics and Mathematical Sciences, Volume 2021, Issue 1, 2021., 2021 In this work, the Catalan transformation (CT) of k‐balancing sequences, Bk,nn≥0, is introduced. Furthermore, the obtained Catalan transformation CBk,nn≥0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k‐balancing sequences, Bk,nn≥0, which is an n × 1 matrix.
Asim Patra +2 more
wiley +1 more source
-Jacobsthal-Lucas hybrid numbers
, 2021 In this paper, we consider the k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. We obtain the Binet formulas, generating functions, exponential generating functions and summation formulas of k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. Also, we
Nayil Kilic, KILIÇ, Nayil
core +1 more source
A new approach to Jacobsthal, Jacobsthal-Lucas numbers and dual vectors [PDF]
, 2023 This paper gives a detailed study of a new generation of dual Jacobsthal and dual Jacobsthal-Lucas numbers using dual numbers. Also some formulas, facts and properties about these numbers are presented.
Faik Babadağ, Babadağ, Faik
core +1 more source
Some Properties between Mersenne, Jacobsthal and Jacobsthal-Lucas Hybrid Numbers
, 2021 © 2021 Elsevier LtdIn this paper, we define Mersenne hybrid numbers inspired by the definition of hybrid numbers. Then, we give some algebraic properties of Mersenne, Jacobsthal and Jacobsthal-Lucas hybrid numbers.
TAŞCI, DURSUN, SEVGİ, EMRE
core +1 more source
Identities relating six members of the Fibonacci family of sequences
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
doaj +1 more source
On Bicomplex Jacobsthal Numbers
, 2021 In this article, bicomplex Jacobsthal and bicomplex Jacobsthal-Lucas numbers are introduced and some properties related to them are ...
Kilic, NAYİL
core +1 more source
The Third Order Jacobsthal Octonions: Some Combinatorial Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways.
Cerda-Morales Gamaliel
doaj +1 more source
On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions [PDF]
, 2022 summary:We study generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. We present some properties of these quaternions and the relations between the generalized commutative Jacobsthal quaternions and ...
Bród, Dorota +2 more
core +1 more source
On Jacobsthal and Jacobsthal-Lucas Octonions [PDF]
, 2017 WOS:000396095300002Various families of quaternion and octonion number sequences (such as Fibonacci quaternion, Fibonacci octonion, and so on) have been established by a number of authors in many different ways.
Çimen, Cennet Bolat +4 more
core +2 more sources