Do you consider thirteen to be unlucky? I don't, but I'm always surprised at the number of people who do. Regardless, here's how to knit sleeves top down from a modified drop shoulder. It's tidy, it allows the aran patterns to progress uninterrupted to the shoulder, and it's just plain fun. For an overview of the perpendicular join, see here. FYI, I also used it for the saddle shoulders in Glenora.
To double check before you launch into this, you should have an even number of stitches on lengths of waste yarn at the underarms and continuous selvedge stitches all the way up the upper body to the shoulders (now joined by 3-needle BO).
I use a 32" circular for the whole procedure (and also for the rest of the sleeve utilizing the magic loop method). Knit up stitches around the armhole in a ratio of 2 stitches for every 3 rows. Review this tutorial if necessary for where and how to knit up stitches. Whilst doing this, at the two bottom corners of the opening next to the underarm stitches, pick up the running thread and twist it before knitting into it to close any gaps, making each twisted stitch lean toward the underarm. Leave the underarm stitches on the waste yarn; they will be worked into the sleeve one at a time. You should end up with an even number.
Example: my 7-inch tall arm opening produced (29 x 2) sts + (1 x 2) at the corners) = 60 sts total.
At this point, if you haven't done this so far, stop to consider which, if any, aran stitches from the body you want to carry down the sleeves. Remember, it must be a stitch pattern that will look the same whether worked bottom up or top down. My gull stitch cable was ruled out for this reason. I chose to employ my largest cable, the Inishmore Cable, for the sleeves. Centre the cable over the shoulder and place markers around the stitches that will be involved. Note that you will begin, as you did for the body, on a WS chart row. The instructions below for the perpendicular join below are written for a plain stocking stitch sleeve; remember to work your chosen aran stitches in the area you have marked out for them.
Now, working back and forth:
Row 1 (WS): Sl1 wyif, purl to last st, sl1, sl1 from waste yarn, sl2 back onto LH needle and p2tog, turn.
Row 2 (RS): Sl wyib, knit to last st, sl1 knitwise, s1 knitwise from waste yarn, insert LH into last 2 sts to make and SSK, turn.
Rep Rows 1 and 2, cont to work back and forth in this fashion, eating up the underarm sts from the waste yarn until 1 st is left on the waste yarn and 1 sts remains on the needle, then work a double dec as foll: sl2tog knitwise (the 2 remaining sts just described), k1, P2SSO. You should have an odd number of sts left in total for the sleeve. Place a locking st marker in the double decrease and move this up as the sleeve progresses. This will be the start of the round. Yes, from here on you will be working your aran chart in the round, so don't forget that you will be reading EVERY row from right to left for the first time in the knitting of the cardigan.
Here's how the underarm will look after a few more rounds, with the sleeve at the top of the photo:
And here's how the perpendicular join will look when completed.