Say that an ordered triple $(a, b, c)$ is pleasing if:

1. $a$, $b$, and $c$ are in the set $\{ 1, 2, \dots, 17 \}$.
2. Both $b - a$ and $c - b$ are greater than $3$, and at least one of them is equal to $4$.

How many pleasing triples are there?

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