This rangOli has reference to my blog http://www.ikolam.com/node/19696 . In it I mentioned that if the number of dots in the row or column is even, then it is not possible to connect it to the border through the middle point. I was thinking about a solution to this problem. The answer is simple. In such a case, connect not the middle point as in the odd case, but two middle points in the even case to the borders. Then we get connections to the border from all sides and still we have only a single line. A real breakthrough 
Here is an example for a 6 x 5 sOnA pattern. The whole pattern including the borders have 10 x 9 dots. The sOnA pattern itself is indicated in red and the connections as well as the outer border are drawn in pink. Even if the colours are different, the whole pattern consists of just one line. Enjoy!
Regards! - mOhana
