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

A175935

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