2013 AMC 12A Problem 7

The sequence $S_1,$ $S_2,$ $S_3,$ $\ldots,$ $S_{10}$ has the property that every term beginning with the third is the sum of the previous two. That is, $$S_n = S_{n-2} + S_{n-1} \text{ for } n \ge 3.$$ Suppose that $S_9 = 110$ and $S_7 = 42.$ What is $S_4?$