Investigating experimentally a topic (somewhat related to Bernoulli convolutions), I came across families of polynomials and I wonder whether they belong to some well-known family. A closely related family is (I think) related to Pisot numbers, so it is not completely hopeless that my polynomials have some number theoretic property.
The first family is $$F_k(X) = X^{k+3}-2X^{k+2}+X-1 \quad k\ge 0$$ and the second one $$G_k(X) = X^{k+4}-2X^{k+3}+X^{k+2}-1 \quad k\ge 0.$$ Other polynomials I get, who probably belong to families that I do not have identified are $$C(X) = x^6-2X^5+X^3-X^2+X-1 \quad D(X) = X^5-2X^4+X^2-1$$ $$ E(X) = X^6-2X^5+X^4-X^3+X^2-1.$$
Do these polynomials ring a bell to any number theorist, by any chance?
