Journal ArticleDOI
A new family of k-Fibonacci numbers
TLDR
The recurrence relations and the generating functions of the new family for k=2 and k=3 are described, and a few identity formulas for the family and the ordinary Fibonacci numbers are presented.About:
This article is published in Applied Mathematics and Computation.The article was published on 2010-02-01. It has received 68 citations till now. The article focuses on the topics: Fibonacci polynomials & Fibonacci number.read more
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Journal ArticleDOI
A note on generalized k-Horadam sequence
Yasin Yazlik,Necati Taskara +1 more
TL;DR: The properties of the generalized k-Horadam sequence are studied and some of these properties are proved by means of determinant and a generating function is obtained for this sequence.
Journal ArticleDOI
Inversion of k-tridiagonal matrices with Toeplitz structure
Ji-Teng Jia,Ji-Teng Jia,Ji-Teng Jia,Tomohiro Sogabe,Tomohiro Sogabe,Tomohiro Sogabe,Moawwad El-Mikkawy,Moawwad El-Mikkawy,Moawwad El-Mikkawy +8 more
TL;DR: A theoretical result is obtained that under certain assumptions the explicit inverse of a k-tridiagonal Toeplitz matrix can be derived immediately.
Journal ArticleDOI
Fast block diagonalization of k-tridiagonal matrices
TL;DR: A fast algorithm for block diagonalization of k-tridiagonalmatrices and some useful results are provided: e.g., another der-ivation of a very recent result on generalized k-Fibonacci numbers in [M.E. El-Mikkawy,T.A. Sogabe, A new family of k
Journal ArticleDOI
A Generalized Symbolic Thomas Algorithm
TL;DR: Two new efficient and reliable computational algorithms are given that are suited for implementation using computer algebra systems such as Mathematica, Macsyma and Maple.
Journal ArticleDOI
A note on h(x) − Fibonacci quaternion polynomials
TL;DR: In this paper, a Binet-style formula, ordinary generating function and some basic identities for the h ( x ) − Fibonacci quaternion polynomial sequences are presented.
References
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Journal Article
The On-Line Encyclopedia of Integer Sequences.
TL;DR: The On-Line Encyclopedia of Integer Sequences (OEIS) as mentioned in this paper is a database of 13,000 number sequences and is freely available on the Web (http://www.att.com/~njas/sequences/) and is widely used.
Book ChapterDOI
The On-Line Encyclopedia of Integer Sequences
TL;DR: The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
Book
Enumerative Combinatorics
TL;DR: This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.
Book
Fibonacci and Lucas Numbers with Applications
TL;DR: The first 100 Lucas Numbers and their prime factorizations were given in this article, where they were shown to be a special case of the first 100 Fibonacci Numbers and Lucas Polynomials.