So when we taught our lesson in class, we were very sad that there was no "fun formula" to figure out how many partitions of an integer n there are. Even though we have the generating function for partitions (which you all know is pretty much the coolest thing ever!), that still can be pretty time consuming and a lot of work.

So even though this isn't exact, I wanted you all to know that there actually is a pretty good formula for estimating how many partitions there are - and although this is just an estimation, it is really pretty amazing because Hardy and Ramanujan (who you should all read about from Teddy and Dan's posts) kind of just came up with it. There is no real proof and it is just an estimation, they just saw that it worked for regular partitions of integers (geniuses…). They originally came up with p(n) is approximately equal to \frac{exp(\pi[[math]]

2n/3

[[/math]]}{4n[[math]]

3

[[/math]]}

and it was later modified by Redamacher and is now called the Redemacher series, which you can see on this wiki page (it's way more complicated) http://en.wikipedia.org/wiki/Integer_partition. This is so weird and also cool because you wonder how the heck all of this random complicated math gives you the number of partitions of an integer… hmm