Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have no hills of the form ud (a hill is either a ud or a Udd starting at the x-axis).

A108434

Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have no hills of the form ud (a hill is either a ud or a Udd starting at the x-axis).