Let S_{n} be the set of points (x / 2, y / 2) \in \mathbb{R}^{2} such that x, y are odd integers and |x| \leq y \leq 2 n. Let T_{n} be the number of graphs G with vertex set S_{n} satisfying the following conditions:
(1) G has no cycles.
(2) If two points share an edge, then the distance between them is 1.
(3) For any path P=(a, \ldots, b) in G, the smallest y-coordinate among the points in P is either that of a or that of b. However, multiple points may share this y-coordinate.
Find the 100th-smallest positive integer n such that the units digit of T_{3 n} is 4.