1st row: K1,yon,*k5, slip the 2nd,3rd,4th, and 5th sts over the 1st stitch, yon: repeat from * to last st, k1
Yes, this gives 41sts as written.
2nd row: P1, *(p1,yon,k1tbl) all into next st, p1; repeat from * to end.
At the end of this row you should have 81sts. The p1, yon and k1tbl all happen in one stitch so each time you repeat this sequence you gain 2sts. You’ll repeat 20 times and so thats 20x2 for an increase on 40sts or a total of 41+40. Take a look at each stitch and make sure you can see the initial p1 and then the repeat: p1, yarn over and k1tbl, p1. If you name each stitch, you may see where the error is.
Maybe this is the pattern? http://www.ravelry.com/patterns/library/bonnet-10