Consider f(n,m) the number of finite sequences of 1's and 0's such that each sequence that starts at 0, has exactly n 0's and m 1's, and there are not three consecutive 0's or three 1's. Show that if m,n>1, then
f(n,m)=f(n−1,m−1)+f(n−1,m−2)+f(n−2,m−1)+f(n−2,m−2) functional equationfunctionalalgebraSequencecombinatorics