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.

Why were most movies from the late 1890s until the early 1930s only filmed in black and white? there were only a few people who could afford the technology to produce color motion pictures back then. audiences did not want color motion pictures until later. the film used to make color motion pictures often overheated, which was a safety hazard, so it was generally not allowed. color films had to be hand-colored, frame by frame.