Stern Polynomials as Numerators of Continued Fractions
Volume 62 / 2014
Bulletin Polish Acad. Sci. Math. 62 (2014), 23-27
MSC: Primary 11B83.
DOI: 10.4064/ba62-1-3
Abstract
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 $n$.
