Modified Grid Walk

Question

A man walks $n$ blocks north and $3n$ blocks east from his residence at $(0,0)$. How many routes are possible from his home to his office at $(3n, n)$ if he cannot walk two block north consecutively?

It is obvious that the good paths are $\binom{3n}{n}$ but how to calculate the bad paths in this walk which would be any two consecutive blocks north?

Answer 1

Almost every north must be followed by an east, so make the moves east and northeast. The only exception is if the path ends with a north, so count those separately.