Results 41 to 50 of about 133 (111)

Bidimensional Extensions of Cobalancing and Lucas-Cobalancing Numbers

Annales Mathematicae Silesianae
A new bidimensional version of cobalancing numbers and Lucas-balancing numbers are introduced. Some properties and identities satisfied by these new bidimensional sequences are studied.
Chimpanzo J., Otero-Espinar M.V., Borges A., Vasco P., Catarino P.   +4 more
doaj   +1 more source

More on finite sums that involve reciprocals of products of generalized Fibonacci numbers, Integers 14 (2014), #A4. Available at http://www.integers-ejcnt.org/vol14.html. 2010 Mathematics Subject Classification: Primary 11B39; Secondary 11B37. Keywords: r [PDF]

, 2020
In this paper we find closed forms for certain finite sums. In each case the denominator of the summand consists of products of generalized Fibonacci numbers.
R S Melham
core  

Horadam Octonions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
In this paper, first we define Horadam octonions by Horadam sequence which is a generalization of second order recurrence relations. Also, we give some fundamental properties involving the elements of that sequence.
Karataş Adnan, Halici Serpil
doaj   +1 more source

Fibonacci Sums Modulo 5

Annales Mathematicae Silesianae
We develop closed form expressions for various finite binomial Fibonacci and Lucas sums depending on the modulo 5 nature of the upper summation limit. Our expressions are inferred from some trigonometric identities.
Adegoke Kunle, Frontczak Robert, Goy Taras   +2 more
doaj   +1 more source

Generalized Chebyshev Polynomials

Discussiones Mathematicae - General Algebra and Applications, 2018
Let h(x) be a non constant polynomial with rational coefficients. Our aim is to introduce the h(x)-Chebyshev polynomials of the first and second kind Tn and Un. We show that they are in a ℚ-vectorial subspace En(x) of ℚ[x] of dimension n.
Abchiche Mourad, Belbachir Hacéne
doaj   +1 more source

Melham's conjecture on odd power sums of fibonacci numbers [PDF]

, 2016
Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at a certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish
Xie, Matthew H.Y., Sun, Brian Y., Yang, Arthur L.B.   +2 more
core  

On Mersenne Numbers and their Bihyperbolic Generalizations

Annales Mathematicae Silesianae
In this paper, we introduce Mersenne and Mersenne–Lucas bihyperbolic numbers, i.e. bihyperbolic numbers whose coefficients are consecutive Mersenne and Mersenne–Lucas numbers.
Bród Dorota, Szynal-Liana Anetta
doaj   +1 more source

Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices

Special Matrices, 2022
In this article, we determine upper and lower bounds for the spectral radius of nonnegative matrices. Introducing the notion of average 4-row sum of a nonnegative matrix, we extend various existing formulas for spectral radius bounds.
Adam Maria, Aretaki Aikaterini
doaj   +1 more source

On Quaternion Gaussian Bronze Fibonacci Numbers

Annales Mathematicae Silesianae, 2022
In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided.
Catarino Paula, Ricardo Sandra
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A New Proof and Consequences of the Fixed Point Theorem of Matkowski

Annales Mathematicae Silesianae, 2021
In this work it was proved Matkowski’s fixed point theorem. The consequences of this theorem are also presented.
Barcz Eugeniusz
doaj   +1 more source