The sequence of blocks in the first row (LSLLSLSLLSLLS...) is known as the infinite Fibonacci word, and it has several nice characterizations.
First, the least practical, but probably coolest:
Take a square table with side length equal to 1 and place a ball in the bottom-left corner. Hit it at an angle so it touches the right wall of the table $\phi - 1 \approx 0.618$ units above the bottom-right corner. Now note the walls it bounces off of: if it bounces off a vertical wall, write L, if it bounces off a horizontal wall, write S. The sequence you'll write corresponds to the sequence of blocks you'll place.
The Fibonacci-like approach to describing the sequence:
Let $F_1 = L$, $F_2 = LS$. Then if we define $F_n = F_{n-1}+F_{n-2}$ (+ stands for concatenation) we get the sequence L, LS, LSL, LSLLS, LSLLSLSL, ... The "limit" of this sequence as $n \rightarrow \infty$, $F_\infty$, is the infinite Fibonacci word.
The closed-form approach:
The nth block of the sequence is large iff $2 + \lfloor n \phi \rfloor - \lfloor (n+1) \phi \rfloor = 1$$2 + \lfloor n \phi \rfloor - \lfloor (n+1) \phi \rfloor = 0$.