How many $n$-words from the alphabet $A=${$a,b,c,d$} are there such that $a$ and $b$ are never neighbors.

Question

How many $n$-words from the alphabet $A=${$a,b,c,d$} are there such that $a$ and $b$ are never neighbors. $\\$
Source : Problem Solving Strategies by Arthur Engel$\\$
The solution given in the book is related to, forming Recurrence relations. The problem is, I am a bit unfamiliar and to Recurrences so is it possible to solve this problem without using Recurrences ?$\\$
Any help would be appreciated. Thanks !!