Results 21 to 30 of about 10,730 (186)

Square numbers, square pyramidal numbers, and generalized Fibonacci polynomials

Journal of New Results in Science, 2022
In this paper, we derive two interesting formulas for square and square pyramidal numbers. We focus on the linear recurrence relation with constant coefficients for square and square pyramidal numbers.
Adem Şahin
doaj   +1 more source

On Fibonacci (k,p)-Numbers and Their Interpretations

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023
In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to
Berke Cengiz, Yasemin Taşyurdu
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Aitken sequences and generalized Fibonacci numbers [PDF]

Mathematics of Computation, 1985
Consider the sequence(vn)({v_n})generated byvn+1=avn−bvn−1{v_{n + 1}} = a{v_n} - b{v_{n - 1}},n⩾2n \geqslant 2, wherev1=1{v_1} = 1,v2=a{v_2} = a, withaandbreal, of which the Fibonacci sequence is a special case. It is shown that if Aitken acceleration is used on the sequence(xn)({x_n})defined byxn=vn+1/vn{x_n} = {v_{n + 1}}/{v_n}, the resulting ...
McCabe, J. H., Phillips, G. M.
openaire   +1 more source

Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences

Mathematics, 2023
In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k-generalized Fibonacci sequence which are almost repdigits. In particular, we find all k-
Alaa Altassan, Murat Alan
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On the sequences of $(q,k)$-generalized Fibonacci numbers [PDF]

Mathematica Bohemica
We consider a new family of recurrence sequences, the $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers.
Jean Lelis, Gersica Freitas, Alessandra Kreutz, Elaine Silva   +3 more
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An Alternating Sum of Fibonacci and Lucas Numbers of Order k

Mathematics, 2020
During the last decade, many researchers have focused on proving identities that reveal the relation between Fibonacci and Lucas numbers. Very recently, one of these identities has been generalized to the case of Fibonacci and Lucas numbers of order k ...
Spiros D. Dafnis, Andreas N. Philippou, Ioannis E. Livieris   +2 more
doaj   +1 more source

On Linear Differential Equations Involving a Para-Grassmann Variable [PDF]

, 2009
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly.
Mansour, Toufik, Schork, Matthias
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GENERALIZED FIBONACCI NUMBERS AND DIMER STATISTICS [PDF]

Modern Physics Letters B, 2002
We establish new product identities involving the q-analogue of the Fibonacci numbers. We show that the identities lead to alternate expressions of generating functions for close-packed dimers on non-orientable surfaces.
Lu, W. T., Wu, F. Y.
openaire   +3 more sources

Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials

Discrete Dynamics in Nature and Society, 2012
We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci, Mirac Cetin Firengiz, Naim Tuglu   +2 more
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Finite sums that involve reciprocals of products of generalized Fibonacci numbers [PDF]

, 2014
© 2014 Walter de Gruyter GmbH, Berlin/Boston. 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. Furthermore, we express each closed form in terms
Melham, RS
core   +1 more source