Difference equation for a sequence

[Guest]

Consider the sequences made of the letters a, b, c, d,e.
Let yn be the number of such sequences of length n in which no three consecutive
entries are all in the set {a, b}; that is to say, the sequences must not contain any
instances of aaa, aab, aba, . . ..
Find y1, y2, y3 and write a difference equation for yn+3 in terms of yn, yn+1, yn+2

I got y1=5,y2=25,y3=117 not really sure how you create the difference equation?