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 having no pyramids of the first kind (a pyramid of the first kind is a sequence u^pd^p for some positive integer p, starting at the x-axis).

A108452

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 having no pyramids of the first kind (a pyramid of the first kind is a sequence u^pd^p for some positive integer p, starting at the x-axis).