Limits of chromatic zeros of some families of maps

Two families of maps are considered, one consisting of maps with two pentagons separated by n 5-rings, the other of maps with two n-gons separated by two n-rings. For each family, a homogeneous linear recursion is derived for the corresponding family of chromatic polynomials. It is shown that B₅, B₇, and B₁₀ are limits of sequences of zeros from one or another of the families, where $\text{B}{}_{\mathrm{n}}\text{= 2(1+}\text{cos}\text{2π}\text{n}\text{)}$.