Matches in SemOpenAlex for { <https://semopenalex.org/work/W2111756918> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W2111756918 abstract "Let denote the third order linear recursive sequence defined by the initial values a0=a1=0 and a2=1 and the recursion an=pan-1+qan-2+ran-3 if n>=3, where p,q, and r are constants. The are generalized Tribonacci numbers and reduce to the usual Tribonacci numbers when p=q=r=1 and to the 3-bonacci numbers when p=r=1 and q=0. Let Qn(x)=a2x^n+a3x^n^-^1+...+an+1x+an+2, which we will refer to as a generalized Tribonacci coefficient polynomial. In this paper, we show that the polynomial Qn(x) has no real zeros if n is even and exactly one real zero if n is odd, under the assumption that p and q are non-negative real numbers with p>=max{1,q}. This generalizes the known result when p=q=r=1 and seems to be new in the case when p=r=1 and q=0. Our argument when specialized to the former case provides an alternative proof of that result. We also show, under the same assumptions for p and q, that the sequence of real zeros of the polynomials Qn(x) when n is odd converges to the opposite of the positive zero of the characteristic polynomial associated with the sequence an. In the case p=q=r=1, this convergence is monotonic. Finally, we are able to show the convergence in modulus of all the zeros of Qn(x) when p>=1>=q>=0." @default.
- W2111756918 created "2016-06-24" @default.
- W2111756918 creator A5024416044 @default.
- W2111756918 creator A5028347723 @default.
- W2111756918 date "2013-04-01" @default.
- W2111756918 modified "2023-09-23" @default.
- W2111756918 title "Polynomials whose coefficients are generalized Tribonacci numbers" @default.
- W2111756918 cites W1528947174 @default.
- W2111756918 cites W1557452007 @default.
- W2111756918 cites W1980756339 @default.
- W2111756918 cites W1989864200 @default.
- W2111756918 cites W2131146595 @default.
- W2111756918 cites W3198160809 @default.
- W2111756918 cites W2742162337 @default.
- W2111756918 doi "https://doi.org/10.1016/j.amc.2012.12.052" @default.
- W2111756918 hasPublicationYear "2013" @default.
- W2111756918 type Work @default.
- W2111756918 sameAs 2111756918 @default.
- W2111756918 citedByCount "2" @default.
- W2111756918 countsByYear W21117569182018 @default.
- W2111756918 countsByYear W21117569182020 @default.
- W2111756918 crossrefType "journal-article" @default.
- W2111756918 hasAuthorship W2111756918A5024416044 @default.
- W2111756918 hasAuthorship W2111756918A5028347723 @default.
- W2111756918 hasConcept C10138342 @default.
- W2111756918 hasConcept C11413529 @default.
- W2111756918 hasConcept C114614502 @default.
- W2111756918 hasConcept C118615104 @default.
- W2111756918 hasConcept C134306372 @default.
- W2111756918 hasConcept C138885662 @default.
- W2111756918 hasConcept C162324750 @default.
- W2111756918 hasConcept C168773036 @default.
- W2111756918 hasConcept C182306322 @default.
- W2111756918 hasConcept C2777303404 @default.
- W2111756918 hasConcept C2778112365 @default.
- W2111756918 hasConcept C2780813799 @default.
- W2111756918 hasConcept C33923547 @default.
- W2111756918 hasConcept C41895202 @default.
- W2111756918 hasConcept C50522688 @default.
- W2111756918 hasConcept C54355233 @default.
- W2111756918 hasConcept C72169020 @default.
- W2111756918 hasConcept C86803240 @default.
- W2111756918 hasConcept C90119067 @default.
- W2111756918 hasConcept C94020503 @default.
- W2111756918 hasConceptScore W2111756918C10138342 @default.
- W2111756918 hasConceptScore W2111756918C11413529 @default.
- W2111756918 hasConceptScore W2111756918C114614502 @default.
- W2111756918 hasConceptScore W2111756918C118615104 @default.
- W2111756918 hasConceptScore W2111756918C134306372 @default.
- W2111756918 hasConceptScore W2111756918C138885662 @default.
- W2111756918 hasConceptScore W2111756918C162324750 @default.
- W2111756918 hasConceptScore W2111756918C168773036 @default.
- W2111756918 hasConceptScore W2111756918C182306322 @default.
- W2111756918 hasConceptScore W2111756918C2777303404 @default.
- W2111756918 hasConceptScore W2111756918C2778112365 @default.
- W2111756918 hasConceptScore W2111756918C2780813799 @default.
- W2111756918 hasConceptScore W2111756918C33923547 @default.
- W2111756918 hasConceptScore W2111756918C41895202 @default.
- W2111756918 hasConceptScore W2111756918C50522688 @default.
- W2111756918 hasConceptScore W2111756918C54355233 @default.
- W2111756918 hasConceptScore W2111756918C72169020 @default.
- W2111756918 hasConceptScore W2111756918C86803240 @default.
- W2111756918 hasConceptScore W2111756918C90119067 @default.
- W2111756918 hasConceptScore W2111756918C94020503 @default.
- W2111756918 hasLocation W21117569181 @default.
- W2111756918 hasOpenAccess W2111756918 @default.
- W2111756918 hasPrimaryLocation W21117569181 @default.
- W2111756918 hasRelatedWork W168650769 @default.
- W2111756918 hasRelatedWork W1977363530 @default.
- W2111756918 hasRelatedWork W1990139562 @default.
- W2111756918 hasRelatedWork W2018318624 @default.
- W2111756918 hasRelatedWork W2031129895 @default.
- W2111756918 hasRelatedWork W2048202079 @default.
- W2111756918 hasRelatedWork W2073769769 @default.
- W2111756918 hasRelatedWork W2083855004 @default.
- W2111756918 hasRelatedWork W2129486468 @default.
- W2111756918 hasRelatedWork W2236798102 @default.
- W2111756918 hasRelatedWork W2279883250 @default.
- W2111756918 hasRelatedWork W2545066301 @default.
- W2111756918 hasRelatedWork W2729443706 @default.
- W2111756918 hasRelatedWork W2774752345 @default.
- W2111756918 hasRelatedWork W2949143588 @default.
- W2111756918 hasRelatedWork W3103853013 @default.
- W2111756918 hasRelatedWork W3114561530 @default.
- W2111756918 hasRelatedWork W3132706803 @default.
- W2111756918 hasRelatedWork W3152324296 @default.
- W2111756918 hasRelatedWork W2186069129 @default.
- W2111756918 isParatext "false" @default.
- W2111756918 isRetracted "false" @default.
- W2111756918 magId "2111756918" @default.
- W2111756918 workType "article" @default.