I didn't realize that you were following a specific pattern, I thought you were trying to imitate a seed stitch border that you had seen somewhere.
You are casting on 228 stitches, or 38 repeats of "k3p3" stitches. Does the pattern you are following ALSO have an even # of stitches divisible by 6? Or perhaps it has an extra 3 stitches cast on? I'm just guessing here...
For seed stitch, you can alternate knitting the purl stitches and purling the knit stitches (1)Every Row, or (2)Every OTHER Row, depending on what look you prefer. Variations in stitches are what makes knitting so much fun
But unless you alternate your stitches I don't see how you'd end up with a seed stitch.
If the pattern you are following casts on a number divisble by 3, but not divisible by 6, I can understand. In that case, you are alternating your knit/purl stitches every row instead of every other row.
Try this: cast on 9 stitches, then follow your pattern. Next, cast on 12 stitches, and again follow your pattern. *don't worry about knitting purl stitches or any of that, just follow the pattern you listed above*
Hope I haven't confused the issue -