Results 21 to 30 of about 48,003 (223)

Some properties of k-generalized Fibonacci numbers

Mathematica Montisnigri, 2021
Fn (k) = (Fm) (Fm+1) r , n = mk + r. In [14], Özkan et al. defined a new family of k-Lucas numbers and gave some identities of the new family of k-Fibonacci and k-Lucas numbers. Özkan et al.
N. Yılmaz, A. Aydoğdu, E. Özkan
semanticscholar   +2 more sources

Generalized Heisenberg algebras and k-generalized Fibonacci numbers [PDF]

Journal of Physics A: Mathematical and Theoretical, 2007
It is shown how some of the recent results of de Souza et al. [1] can be generalized to describe Hamiltonians whose eigenvalues are given as k-generalized Fibonacci numbers.
Curado E M F, de Souza J, Dubeau F, Dubeau F, Fuller L E, Hoggatt V E, Lee G-Y, Lee G-Y, Levesque C, Matthias Schork, Mouline M, Mouline M, Philippou A N, Turban L, Turban L   +14 more
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Generalized Fibonacci Numbers: Sum Formulas

Journal of Advances in Mathematics and Computer Science, 2020
In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.
Y. Soykan
semanticscholar   +4 more sources

On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers

Advances in Research, 2019
In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results.
Y. Soykan
semanticscholar   +4 more sources

On the self-convolution of generalized Fibonacci numbers

, 2017
We focus on a family of equalities pioneered by Zhang and generalized by Zao and Wang and hence by Mansour which involves self convolution of generalized Fibonacci numbers.
Belbachir, Hacène, Djellal, Toufik, Luque, Jean-Gabriel   +2 more
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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 ...
J. H. McCabe, G. M. Phillips
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Closed Formulas for the Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Σn k=0W3 Σ k and n k=1W3

, 2020
In this paper, closed forms of the sum formulas for the cubes of generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas numbers.
Y. Soykan
semanticscholar   +3 more sources

Transformations of Pythagorean triples generated by generalized Fibonacci numbers [PDF]

Notes on Number Theory and Discrete Mathematics
We present matrices that transform Pythagorean triples arising from generalized Fibonacci sequences into other such triples. We also show that entries in the powers of such matrices can be expressed in terms of generalized Fibonacci sequences.
Jathan Austin
semanticscholar   +2 more sources

A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3} $

, 2020
W n = r s W (n 1) + 1 s W (n 2) for n = 1; 2; 3; ::: when s 6= 0: Therefore, recurrence (1.1) holds for all integer n: 1 be extended to negative subscripts by de…ning these generalized Fibonacci numbers fWn(a; b; r; s)g are also called Horadam numbers ...
Y. Soykan
semanticscholar   +3 more sources

Generalized a:k:m-Fibonacci Numbers [PDF]

Asian Research Journal of Mathematics, 2018
Lovemore Mamombe
openalex   +2 more sources