Number of lattice paths from (0,0) to (n,n) using steps S={(1,0),(0,1),(r,r)|0<r<=2} that never go above the line y=x.

A175934

Number of lattice paths from (0,0) to (n,n) using steps S={(1,0),(0,1),(r,r)|0<r<=2} that never go above the line y=x.