Question

# Consider binary strings with n digits (for example, if n=4, some of the possible strings are 0011,1010,1101, etc.) Let Zn be the number of binary stri

Bivariate numerical data
Consider binary strings with n digits (for example, if n=4, some of the possible strings are 0011,1010,1101, etc.)
Let Zn be the number of binary strings of length n that do not contain the substring 000
Find a recurrence relation for Zn
You are not required to find a closed form for this recurrence.

This covers all cases. Therefore, the recurrence relation is $$Zn=Zn-1+Zn-2+Zn-3$$