Here The strings of length one (a1) and which do not have two consecutive Zeros
0,1
The strings of length two (a2) and which do not have two consecutive Zeros,
01,10,11
The strings of length three (a3) and which do not have two consecutive Zeros,
010 ,011, 101, 110, 111
The strings of length four (a4) and which do not have two consecutive Zeros,
0101 , 0110 , 0111 , 1010 , 1011, 1101, 1110, 1111
Clearlly here a1=2
a2=3
a3=a1+a2=5
a4=a3+a2=8
So recurance relation a(n)=a(n-1)+a(n-2) for n>=3