Assignment:
If n >= 1, the number of strings using the digits 0,1, and 2 with no two consecutive places holding the same digit, is 3x2^n-1. For example, there are 12 such strings of length three: 010, 012, 020, 021, 101, 102, 120, 121, 201, 202, 210, and 212.
Prove this claim by induction on the length of the strings. Is the formula true for n=0?
Provide complete and step by step solution for the question and show calculations and use formulas.