3. As shown in Figure 1, in Yang

Hui's triangle, above the diagonal line $l$,
starting from 1, the numbers indicated by
the arrow form a zigzag sequence:
$1,3,3,4,6,5,10$, $\cdots$, let the sum of the first $n$ terms be $S_{n}$. Then the value of $S_{17}$ is ( ).
(A) 172
(B) 217
(C) 228
(D) 283
3. B.

By the properties of combinations, the sequence $1,3,3,4,6,5,10, \cdots$ is actually composed of $\mathrm{C}_{2}^{2}, \mathrm{C}_{3}^{1}, \mathrm{C}_{3}^{2}, \mathrm{C}_{4}^{1}, \mathrm{C}_{4}^{2}, \mathrm{C}_{5}^{1}, \mathrm{C}_{5}^{2}, \cdots$. Therefore,
$$
\begin{array}{l}
S_{17}=C_{2}^{2}+C_{3}^{1}+C_{3}^{2}+C_{4}^{1}+C_{4}^{2}+\cdots+C_{10}^{1}+C_{10}^{2} \\
=C_{3}^{3}+C_{3}^{2}+C_{4}^{2}+\cdots+C_{10}^{2}-C_{3}^{2}+C_{3}^{2}+C_{3}^{1}+\cdots+C_{10}^{1} \\
=C_{11}^{3}+C_{11}^{2}-3=217 .
\end{array}
$$