English

Generalizations of some identities involving the fibonacci numbers

Combinatorics 2007-05-23 v1
Authors: Toufik Mansour
View on arXiv ↗ PDF ↗

Abstract

In this paper we study the sum ∑j1+j2+...+jd=n∏i=1dFk⋅ji,\sum_{j_1+j_2+...+j_d=n}\prod_{i=1}^d F_{k\cdot j_i}, where d≥2d\geq2 and k≥1k\geq1.

Keywords

fibonacci numbers identities summation generalizations

Cite

@article{arxiv.math/0301157,
  title  = {Generalizations of some identities involving the fibonacci numbers},
  author = {Toufik Mansour},
  journal= {arXiv preprint arXiv:math/0301157},
  year   = {2007}
}

Comments

12 pages

Related papers

View all related →
Number Theory · Mathematics
Generalized Fibonacci sequences and their properties
Martin Bunder, Joseph Tonien
2021-07-01
Number Theory · Mathematics
Fibonacci Numbers as Sums of Consecutive Terms in $k$-Generalized Fibonacci Sequence
Roberto Alvarenga, Ana Paula Chaves, Maria Eduarda Ramos, Matheus Silva +1
2025-01-08
Combinatorics · Mathematics
Partial Sums of the Fibonacci Sequence
Hung Viet Chu
2021-06-08
Combinatorics · Mathematics
Degree $5$ Fibonacci Sums via the Gelin-Ces\`aro Identity
Kunle Adegoke
2023-10-10
Number Theory · Mathematics
Powers of two as sum of two generalized Fibonacci numbers
Diego Marques
2014-09-10
Combinatorics · Mathematics
Theorems and Conjectures on Some Rational Generating Functions
Richard P. Stanley
2021-10-01
Number Theory · Mathematics
Some Weighted Generalized Fibonacci Number Summation Identities, Part 1
M. J. Kronenburg
2019-12-10
General Mathematics · Mathematics
On Concatenations of Two $ k $-Generalized Fibonacci Numbers
Alaa Altassan, Murat Alan
2024-07-25
Number Theory · Mathematics
Symmetry properties of finite sums involving generalized Fibonacci numbers
Kunle Adegoke, Oluwaseyi Oshin
2017-10-04
Number Theory · Mathematics
Sums of Squares: Methods for Proving Identity Families
Russell Jay Hendel
2022-05-03
Combinatorics · Mathematics
A Novel Property of Generalized Fibonacci Sequence in Grids
Zixian Yang, Jianchao Bai
2026-04-28
Number Theory · Mathematics
On the sum of reciprocal generalized Fibonacci numbers
Pingzhi Yuan, Zilong He, Junyi Zhuo
2015-03-04
Number Theory · Mathematics
Sums of powers over equally spaced Fibonacci numbers
Helmut Prodinger
2019-07-19
Number Theory · Mathematics
Four New Generalized Fibonacci Number Summation Identities
M. J. Kronenburg
2018-08-30
Number Theory · Mathematics
Some Weighted Generalized Fibonacci Number Summation Identities, Part 2
M. J. Kronenburg
2021-07-14
Combinatorics · Mathematics
Solutions for $k$-generalized Fibonacci numbers using Fuss-Catalan numbers
S. R. Mane
2025-08-27
Number Theory · Mathematics
On the diophantaine equations $J_N +J_M =F_A$ & $F_N +F_M =J_A$
Seif Tarek, Ahmed Gaber, M. Anwar
2022-09-30
General Mathematics · Mathematics
Fibonacci-harmonic sums
Kunle Adegoke, Segun Olofin Akerele, Robert Frontczak
2025-07-29
Number Theory · Mathematics
Linear Properties of Generalized $n$-step Fibonacci Numbers
Kunle Adegoke
2018-08-09
Number Theory · Mathematics
Sums of products of generalized Fibonacci and Lucas numbers
Hacene Belbachir, Farid Bencherif
2007-08-20
Number Theory · Mathematics
On the Diophantine equation $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$
Pagdame Tiebekabe, Ismaïla Diouf
2022-09-27
Combinatorics · Mathematics
Generalized Natural Density $\DF(\mathfrak{F}_n)$ of Fibonacci Word
Jasem Hamoud, Duaa Abdullah
2025-04-15
Combinatorics · Mathematics
A new Fibonacci identity and its associated summation identities
Kunle Adegoke
2018-09-20
General Mathematics · Mathematics
Squares of Fibonacci-Like Numbers
Kunle Adegoke, Tokunbo Omiyinka
2019-01-09
Number Theory · Mathematics
Subsequences and Divisibility by Powers of the Fibonacci Numbers
Kritkajohn Onphaeng, Prapanpong Pongsriiam
2014-05-29