It is proved that the nth Stern polynomial Bₙ(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 Bₙ(1). As an application, the degree of Bₙ(t) is expressed in terms of the binary expansion of n.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-3,
author = {A. Schinzel},
title = {Stern Polynomials as Numerators of Continued Fractions},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {62},
year = {2014},
pages = {23-27},
zbl = {06321109},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-3}
}
A. Schinzel. Stern Polynomials as Numerators of Continued Fractions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) pp. 23-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-3/