Results 71 to 80 of about 1,206 (140)

A Generalization of Jacobsthal and Jacobsthal-Lucas numbers

, 2019
In this paper, we study a generalization of Jacobsthal and Jacobsthal-Lucas numbers, we find their generating function binet formulas, related matrix representation and many other ...
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Binomial sums with k-Jacobsthal and k-Jacobsthal–Lucas numbers

Notes on Number Theory and Discrete Mathematics, 2022
In this paper, we derive some important identities involving k-Jacobsthal and k-Jacobsthal–Lucas numbers. Moreover, we use multinomial theorem to obtain distinct binomial sums of k-Jacobsthal and k-Jacobsthal–Lucas numbers.
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Non-Fisherian generalized Fibonacci numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Using biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
doaj   +1 more source

Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers

, 2013
In this study we define and study the Gaussian Jacob-sthal and Gaussian Jacobsthal Lucas numbers. We give generating functions, Binet formulas, explicit formulas and Q matrix of these numbers. We also present explicit combinatorial and determinantal expressions, study negatively subscripted numbers and give various identities. Similar to the Jacobsthal
Aşçı, Mustafa, Gürel, Eşref
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Triangle Geometry and Jacobstahl Numbers [PDF]

Irish Mathematical Society Bulletin, 2003
The author studies convergence properties of certain triangle centres on the Euler line of an arbitrary triangle. Properties of the Jacobsthal numbers, which appear in this process, are examined.
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Bicomplex Third-order Jacobsthal Quaternions

, 2018
The aim of this work is to consider the bicomplex third-order Jacobsthal quaternions and to present some properties involving this sequence, including the Binet-style formulae and the generating functions.
Cerda, Gamaliel
core  

A New Generalization of Jacobsthal Lucas Numbers (Bi-Periodic Jacobsthal Lucas Sequence)

Journal of Advances in Mathematics and Computer Science, 2020
In this study, we bring into light a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as   with initial conditions $$\ \hat{c}_{0}=2,\ \hat{c}_{1}=a.$$ The Binet formula as well as the generating function for this sequence are given.
Evans Owusu, Sukran Uygun
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On characteristic polynomial of higher order generalized Jacobsthal numbers

Advances in Difference Equations, 2019
In this paper, we study a higher order generalization of the Jacobsthal sequence, namely, the (k,c) $(k,c)$-Jacobsthal sequence (Jn(k,c)) $(J^{(k,c)}_{n})$ for any integers n, k≥2 $k\geq 2$ and a real number c>0 $c>0$.
Diego Marques, Pavel Trojovský
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A combined approach to Perrin and Padovan hybrid sequences. [PDF]

Heliyon, 2021
Jafari Petroudi SH, Pirouz M, Karaca E, Yılmaz F.   +3 more
europepmc   +1 more source

Binomial Transforms of the Third-Order Jacobsthal and Modified Third-Order Jacobsthal Polynomials

Universal Journal of Mathematics and Applications
In this study, we define the binomial transforms of third-order Jacobsthal and modified third-order Jacobsthal polynomials. Further, the generating functions, Binet formulas and summation of these binomial transforms are found by recurrence relations ...
Gamaliel Morales
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