I will be glad to share what I know about the #(N)'s designation. Most plants are by nature, 2(N) - often referred to as diploid; this means that their DNA is composed of 2 strands. Some plants will naturally mutate into 4(N) strains, referred to as tetraploid; this means that their DNA is composed of 4 strands. This somewhat 'doubles' the DNA's effect on the plant - often making it more vigorous, with larger, more substantial flowers. This is really obvious in Daylilies as the "old-fashioned" diploid strains are rather small and have petals that are similar to tissue-paper; tetraploid daylilies often have HUGE flowers that are very thick petaled and the plants often grow very lush and strong.
Tetraploid plants can be achieved by breeding 4(N) X 4(N) or treating the seeds with strong mutagenic chemicals such as Ethyl methanesulfonate (EMS) or Dimethyl Sulfanate; radiation can also be used. Many of our crop plants, such as corn, have been mutagenically modified to increase crop yields, disease resistance and drought resistance.
Now, about the odd numbered (N)s. When you breed a 2(N) with a 4(N), you get a 3(N), referred to as a triploid or a "craploid"; they are often weak, sterile and seldom achieve high standards. But as in all things, there are exceptions. I recently ran across and Ad for a 3(N) SLC that was beautiful and EXPENSIVE. As someone looking for superior breed stock, it held no interest for me as it could be sterile or would throw inferior plants; but, this plant was obviously throwing it's strongest traits out and was, again, a beautiful example.
Are there 5(N), 6(N), etc? Rule out nothing in the plant world. It is my understanding that as long as the (N) is even numbered, most of the progeny should be outstanding. But if there is an odd DNA strand, resulting in an odd (N) number, the results are unstable.
Now - the unspoken questions - How do you know the (N) of a plant? It can be detected using proper lab equipment, but when purchasing, unless you have a portable lab, you have to just trust the seller to be honest with you about it. You can look at the breeding, and as long as the parents were 4(N), you should have a 4(N) plant - but again, unless you can check the DNA strands or the seller offers some proof that such a test was run on the parents, you just have to trust their word. Sometimes the plant will look amazingly stronger, larger bloomed, better substance, etc, but looks can never be trusted to determine DNA. It is a shame that there is not documentation provided for all 4(N) lines as they are often sold for considerably more than their 2(N) relatives. I have seen 10X price increase in one case - BLC. Ports of Paradise 4(N) - approx. $30.00 for a 2(N) division - $300.00 for a 4(N) division.
Does that help? If others have more to add or if I have represented something incorrectly, please provide input / correction. I would appreciate it.
Have a great day -