JPortman: It seems to me like there's one more valid solution in this problem. The first move can be made not only at any of 2-1 points (A18 or B19), but also at any of 3-1 points (A17 or C19). The sequence that follows will be a bit longer, but it will also lead to the "bent four in the corner" (magari shimoku). The sequence I'm talk8ng about is: A17-B17-B19-A19-A18-A19-A18 - a series of snapbacks around 1-1 point. I hope I've described the sequence clear enough. :)
Your moves have been added.