$(6\%)$ Messages are sent over a communications channel using two different signals. One signal requires $2$ microseconds for transmittal, and the other signal requires $3$ microseconds for transmittal. Each signal of a message is followed immediately by the next signal. $($a$)(3\%)$ Find a recurrence relation for the number of different signals that can be sent in n microseconds. $($b$)(1\%)$ What are the initial conditions of the recurrence relations in part $($a$)?($c$)(2\%)$ How many different messages can be sent in $12$ microseconds?