A Matrix Related to Stern Polynomials and the Prouhet-Thue-Morse Sequence

George Beck, Karl Dilcher

The Stern polynomials defined by $s(0;x)=0$, $s(1;x)=1$, and for $n\ge 1$ by $s(2n;x)=s(n;x^2)$ and $s(2n+1;x)=xs(n;x^2)+s(n+1;x^2)$ have only 0 and 1 as coefficients. We constr…