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Note on the sequence A157751
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | THIÉRY, Alain | |
dc.date.accessioned | 2024-04-04T03:22:42Z | |
dc.date.available | 2024-04-04T03:22:42Z | |
dc.date.created | 2011-06-28 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194779 | |
dc.description.abstractEn | In this note, the following \href{http://oeis.org/A157751}{conjecture of Clark Kimberling}(?) is proved \begin{conjecture} Let $(F_n(X))_{n\in \N}$ be the sequence of polynomials defined by $F_n(X) = (X+1)F_{n-1}(X)+F_{n-1}(-X)$ with initial term $F_0(X) = 1$. If $n$ is even then $F_n(X)$ has no real roots, and if $n$ is odd then $F_n(X)$ has exactly one real root, denoted by $r$, and if $n\ges 5$ then $0 < -r < n$. \end{conjecture} | |
dc.language.iso | en | |
dc.title.en | Note on the sequence A157751 | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
hal.identifier | hal-01003701 | |
hal.version | 1 | |
hal.audience | Non spécifiée | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-01003701v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=THI%C3%89RY,%20Alain&rft.genre=preprint |
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