Geodesic
Stern Polynomials as Numerators of Continued Fractions
A. Schinzel1
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) no. 1, pp. 23-27

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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 $n$.
DOI : 10.4064/ba62-1-3
Keywords: proved nth stern polynomial sense klav milutinovi petr adv appl math numerator continued fraction terms generalizes result graham knuth patashnik concerning stern sequence application degree expressed terms binary expansion nbsp

A. Schinzel 1

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland 
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A. Schinzel. Stern Polynomials as Numerators of Continued Fractions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) no. 1, pp. 23-27. doi: 10.4064/ba62-1-3

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