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Stern Polynomials as Numerators of Continued Fractions

Volume 62 / 2014

A. Schinzel Bulletin Polish Acad. Sci. Math. 62 (2014), 23-27 MSC: Primary 11B83. DOI: 10.4064/ba62-1-3


It is proved that the $n$th Stern polynomial $B_{n}(t)$ in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of $n$ terms. This generalizes a result of Graham, Knuth and Patashnik concerning the Stern sequence $B_n(1)$. As an application, the degree of $B_n(t)$ is expressed in terms of the binary expansion of $n$.


  • A. SchinzelInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland

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