Number of returns to the x-axis (i.e., d or u steps hitting the x-axis) in all Grand Motzkin paths of length n. (A Grand Motzkin path of length n is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).).

A109194

Number of returns to the x-axis (i.e., d or u steps hitting the x-axis) in all Grand Motzkin paths of length n. (A Grand Motzkin path of length n is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).).