For a natural number $n \geq 2$, consider the set
$$\left\{ 3 ^ { 2 k - 1 } \mid k \text{ is a natural number, } 1 \leqq k \leqq n \right\}$$
Let $S$ be the set containing only all possible values obtained by multiplying two distinct elements of this set, and let $f ( n )$ be the number of elements in $S$. For example, $f ( 4 ) = 5$. Find the value of $\sum _ { n = 2 } ^ { 11 } f ( n )$. [4 points]