Base Case for the Recursion

#1

What should be the base case for the recurrence
relation

#2

base case should be
if n==0
return 1;
if n==1
return 2

#3

shouldn’t it be 0 for n=0 as per the meaning of the state
ie number of binary strings of length 0 ( N=0 ) which have no consecutive ones

#4

an empty string can also be considered as a valid case because it satisfies the condition.