jmc

We solve by casework.

$\bullet$ Case I: Exactly one T in the sequence. There are $3$ slots in which the $T$ could be placed. Then, there are $4$ choices $(A,$ $R,$ $G,$ or $E)$ for the second slot and $3$ for the third, giving a total of $3\cdot 4\cdot 3=36$ sequences.

$\bullet$ Case II: Exactly two Ts in the sequence. There are $3$ slots in which the non-$T$ can be placed, and there are $4$ possibilities for the letter choice. So, there are a total of $3\cdot 4=12$ such sequences.

Thus, there are $36+12=\boxed{48}$ possible sequences.