English

Evaluation of weighted Fibonacci sums of a certain type

General Mathematics 2018-03-09 v2
Authors: Kunle Adegoke
View on arXiv ↗ PDF ↗

Abstract

We derive a formula for the evaluation of weighted generalized Fibonacci sums of the type Skn(w,r)=∑j=0kwjjrGjnS_k^n (w,r) = \sum_{j = 0}^k {w^j j^r G_j{}^n }. Several explicit evaluations are presented as examples.

Keywords

fibonacci sums weighted sums generalized fibonacci evaluation formula

Cite

@article{arxiv.1803.00921,
  title  = {Evaluation of weighted Fibonacci sums of a certain type},
  author = {Kunle Adegoke},
  journal= {arXiv preprint arXiv:1803.00921},
  year   = {2018}
}

Comments

13 pages, no figures, no tables

Related papers

View all related →
Classical Analysis and ODEs · Mathematics
Weighted generalized Fibonacci sums
Kunle Adegoke
2018-05-07
Number Theory · Mathematics
Generalized Fibonacci sequences and their properties
Martin Bunder, Joseph Tonien
2021-07-01
Number Theory · Mathematics
A summation formula for generalized $k$-bonacci numbers
Jean-Christophe Pain
2022-11-02
Number Theory · Mathematics
Some Weighted Generalized Fibonacci Number Summation Identities, Part 1
M. J. Kronenburg
2019-12-10
Number Theory · Mathematics
Some Weighted Generalized Fibonacci Number Summation Identities, Part 2
M. J. Kronenburg
2021-07-14
Number Theory · Mathematics
The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences
Yongkang Wan, Zhonghao Liang, Qunying Liao
2025-09-19
Classical Analysis and ODEs · Mathematics
Weighted Tribonacci sums
Kunle Adegoke
2018-04-19
Combinatorics · Mathematics
Sums of Powers of Fibonacci and Lucas Polynomials in terms of Fibopolynomials
Claudio de Jesus Pita Ruiz Velasco
2013-03-07
General Mathematics · Mathematics
On the Sum of the Sixth Powers of Fibonacci Numbers
Kunle Adegoke, Olawanle Layeni
2024-01-19
Combinatorics · Mathematics
Generalizations of some identities involving the fibonacci numbers
Toufik Mansour
2007-05-23
Number Theory · Mathematics
Elementary methods for evaluating Jordan's sums and analogous Euler's type sums and for setting a sigma sum theorem
Guy Bastien
2013-02-01
Number Theory · Mathematics
Weighted sums of some second-order sequences
Kunle Adegoke
2018-04-13
Number Theory · Mathematics
Weighted sums of Lucas numbers of the first and second kind
aBa Mbirika
2025-11-24
Combinatorics · Mathematics
Partial Sums of the Fibonacci Sequence
Hung Viet Chu
2021-06-08
Combinatorics · Mathematics
Sums of $k$-bonacci Numbers
Harold R. Parks, Dean C. Wills
2022-08-03
Combinatorics · Mathematics
The asymptotic estimation for two classes of generalized Fibonacci sub-sequences
Yongkang Wan, Zhonghao Liang, Qunying Liao
2025-10-16
Combinatorics · Mathematics
Degree $5$ Fibonacci Sums via the Gelin-Ces\`aro Identity
Kunle Adegoke
2023-10-10
Combinatorics · Mathematics
Partial sums of the Gibonacci sequence
Pankaj Jyoti Mahanta
2021-09-09
Number Theory · Mathematics
On the sum of reciprocal generalized Fibonacci numbers
Pingzhi Yuan, Zilong He, Junyi Zhuo
2015-03-04
Number Theory · Mathematics
Powers of two as sum of two generalized Fibonacci numbers
Diego Marques
2014-09-10
Number Theory · Mathematics
Weighted sum formulas of multiple t-values with even arguments
Zhonghua Li, Ce Xu
2019-08-09
Number Theory · Mathematics
Sums of products of generalized Fibonacci and Lucas numbers
Hacene Belbachir, Farid Bencherif
2007-08-20
Number Theory · Mathematics
On Evaluation of Nonlinear Exponential Sums
N. A. Carella
2007-05-23
Combinatorics · Mathematics
On Ledin and Brousseau's summation problems
Kunle Adegoke
2022-08-02
Number Theory · Mathematics
Sums of powers over equally spaced Fibonacci numbers
Helmut Prodinger
2019-07-19