Round 3: Problem 4

Each CUNY Math Challenge participant is allocated a 50-digit identification number. The I.D. number must start with a 1 and only use the digits 0 and 1. Moreover, it may not contain two consecutive 1s or three consecutive 0s. How many different identification numbers that meet these requirements are possible?

Submissions for round 3 are due by Sunday, April 12 at 11:59 p.m. Solution will be posted (if we solve it) immediately after submissions are over.