A046171 Number of inequivalent self-avoiding walks of length n on a 2-D lattice which start at origin, take first step in {+1,0} direction and if any steps are vertical, a step up is taken before a step down.

1, 2, 5, 13, 36, 98, 272, 740, 2034, 5513, 15037, 40617, 110188, 296806, 802075, 2155667, 5808335, 15582342, 41889578, 112212146, 301100754, 805570061, 2158326727, 5768299665, 15435169364, 41214098278, 110164686454