(In reply to

solution by Charlie)

**Your result is correct, and it can be easily explained:**

the number **a(n)** must cover all the qualifying subsets of **n-1** integers i.e, ** a(n-1)** plus all the qualifying subsets of** n-2** elements, where to each of them integer **n** was added (the integer **n-1** is absent!).

**a(n)= a(n-1)** +** a(n-2)**

**a(1)=2=f(3) so a(n)=f(n+2)**