Let S(n) be the number of binary strings of length n that avoid the substring 111 meaning there are no 3 consecutive bits that are all 1. For example, if n=5 then 01101 avoids the substring 111 but 01110 does not avoid the substring 111. Compute T(0), T(1), T(2), T(3), T(4) by writing down all the strings.
