$q$-Stern Polynomials as Numerators of Continued Fractions
Tom 63 / 2015
Bulletin Polish Acad. Sci. Math. 63 (2015), 11-18 MSC: 11B37, 11B75, 11B83. DOI: 10.4064/ba63-1-2
We present a $q$-analogue for the fact that the $n$th Stern polynomial $B_n(t)$ in the sense of Klav\v zar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of $n$ terms. Moreover, we give a combinatorial interpretation for our $q$-analogue.