AMC 12B 2019 Problem 23

How many sequences of 0 s and 1 s of length 19 are there that begin with a 0 , end with a 0 , contain no two consecutive 0 s, and contain no three consecutive 1 \mathrm{~s} ?

Answer Choices
A. 55
B. 60
C. 65
D. 70
E. 75