You meanngreaterthan 1 (nless than 1 makes no sense).

Well, forn= 2, w(2) = (since all words are possible exceptaa).

Forn> 2, first find the number ofn-letter words beginning witha. The second letter must beb,c,dore. The number ofn-letter words beginning withabis w(n−2). This is also the number ofn-letter words beginning withac,adorae. Hence the total number ofn-letter words beginning withais 4w(n−2).

The numbern-letter words beginning withbis w(n−1). This is also the number ofn-letter words beginning withc,dore. Hence the total number ofn-letter words not beginning withais 4w(n−1).

Therefore, the recurrence relation is w(1) = 5, w(2) = 24 and w(n) = 4[w(n−1)+w(n−2)] forn> 2.