Log-concavity conjecture for Clar covering polynomials

Let $H$ be a hexagonal system, and let its Clar covering polynomial be

$$\chi(H,x)=\sum_{k=0}^{C(H)}c(H,k)x^k,$$

where $c(H,k)$ is the number of Clar covers of $H$ having precisely $k$ hexagons. Log-concavity conjecture for Clar covering polynomials. The Clar covering polynomial of a hexagonal system has log-concave coefficients. Numerical results motivate this conjecture, which is presented as open in the source.