I was working on a cool maths problem and got inspired from one of the mini lemmas I had to make up in order to solve the problem. From then on, I have been trying to find a formula which for any positive integer, gives the number of ways it can be "built" as a sum of smaller positive integers. Example: for 5, you can have: 1+1+3, 2+3, 1+4, 1+1+1+1+1, etc.
Finding a formula that regards (example) 1+1+3, 3+1+1 and 1+3+1 as unique "constructions" proved to be not too hard (in fact I re-discovered ;P 2 formulas) but finding a formula for my original aim is proving exceedingly difficult for me.
Please (I don't wan't to spoil the fun and look the answers up on wikipedia or something), given a high school education in maths, could one potentially attain the formula (as I have been trying for very long now) or am I wasting my time and should I look up the answer (as it is far too advanced???)? Thank you.