ON DETERMINANTS OF SOME TRIDIAGONAL MATRICES CONNECTED WITH FIBONACCI NUMBERS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F13%3A50001530" target="_blank" >RIV/62690094:18470/13:50001530 - isvavai.cz</a>
Result on the web
<a href="http://www.ijpam.eu/contents/2013-88-4/11/11.pdf" target="_blank" >http://www.ijpam.eu/contents/2013-88-4/11/11.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.12732/ijpam.v88i4.11" target="_blank" >10.12732/ijpam.v88i4.11</a>

Result language
angličtina
Original language name
ON DETERMINANTS OF SOME TRIDIAGONAL MATRICES CONNECTED WITH FIBONACCI NUMBERS
Original language description
The Fibonacci sequence (or sequence of Fibonacci numbers) ( F_n) is the sequence of positive integers satisfying the recurrence F_n+2=F_n+1+F_n with the initial conditions F_0=0 and F_1= 1. The Lucas sequence is a sequence ( L_n) of positive integers satisfying the same recurrence as Fibonacci numbers but with the initial conditions L_0=2 and L_1=1. These sequences are usually extended for negative indices by identities F_{-n}=(-1)^{n+1}F_{n} and L_{-n}=(-1)^{n}L_{n}. We will concentrate on review of some facts on Fibonacci numbers, Hessenberg matrices and tridiagonal matrices in this paper. We will summarize the results on determinants of families of tridiagonal matrices which have as the value some Fibonacci numbers, but we prove most of this resultsby simpler and more direct way with the help of The On-line Encyclopedai of Integer Sequences (OEIS).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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