2019 AIME II Problem 2

Lily pads 1,2,3,\ldots lie in a row on a pond. A frog makes a sequence of jumps starting on pad 1. From any pad k the frog jumps to either pad k+1 or pad k+2 chosen randomly with probability \tfrac{1}{2} and independently of other jumps. The probability that the frog visits pad 7 is \tfrac{p}{q}, where p and q are relatively prime positive integers. Find p+q.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.