hi i am trying to solve this recrrence relation is tough!!

given this question, i had no idea how to define the condition to start!

can someone help me!!? I understand is an-1 for different cases !

A string that contains only 0s, 1s, 2s and 3s is called a quaternary string.

i) Find a recurrence relation for the number of quaternary strings that do not contain two consecutive zeros.

ii)Solve the recurrence relation