Cancellation in cyclic consecutive systems

We consider the structure and number of non-zero terms in the reliability polynomials for cyclic consecutive systems. We explain the large amount of cancellation, the fact that all but one of the coefficients are 0, 1 or −1, and show that the number of non-zero coefficients is asymptotic to αk, where α is the largest root of 2+xr−xr+1=0.