DC FieldValueLanguage
dc.contributor.authorStević, Stevoen_US
dc.contributor.authorIričanin, Bratislaven_US
dc.contributor.authorKosmala, Witolden_US
dc.contributor.authorŠmarda, Zdeněken_US
dc.date.accessioned2020-10-05T07:32:26Z-
dc.date.available2020-10-05T07:32:26Z-
dc.date.issued2020-09-10-
dc.identifier.issn1687-1847-
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/4141-
dc.description.abstractIt is known that every solution to the second-order difference equation xn= xn−1+ xn−2= 0 , n≥ 2 , can be written in the following form xn= xfn−1+ x1fn, where fn is the Fibonacci sequence. Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also present an interesting elementary procedure for finding a representation of general solution to any homogeneous linear difference equation with constant coefficients in terms of the coefficients of the equation, initial values, and an extension of the Fibonacci sequence. This is done for the case when all the roots of the characteristic polynomial associated with the equation are mutually different, and then it is shown that such obtained representation also holds in other cases. It is also shown that during application of the procedure the extension of the Fibonacci sequence appears naturally.en_US
dc.subjectFibonacci sequence | General solution | Homogeneous linear difference equation with constant coefficients | Representation of solutionsen_US
dc.titleNote on some representations of general solutions to homogeneous linear difference equationsen_US
dc.typeArticleen_US
dc.identifier.doi10.1186/s13662-020-02944-y-
dc.identifier.scopus2-s2.0-85091356448-
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Artsen_US
dc.relation.firstpageArticle no. 486-
dc.relation.issue1-
dc.relation.volume2020-
dc.description.rankM21a-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0002-7202-9764-

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