Gorf the frog is standing on the first lily pad in a row of lily pads numbered from $1$ to $20$ from left to right. On a single jump, Gorf can jump either $1$, $2$, or $3$ lily pads to the right. Unfortunately, all the prime-numbered lily pads are contaminated with deadly poison. How many sequences of jumps allow Gorf to jump to the twentieth lily pad while avoiding the poison?

Let's think step by step and output the final answer within \boxed{}.
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