I then got some very helpful emails pointing me to the vast math literature on this problem. I was not surprised there was such a literature, though I was surprised I hadn't found any of it searching the web.
The literature didn't have my formula, though it had several ways to derive it (some faster than mine).
Why isn't the formula out there? Why couldn't I find the literature?
- The formula falls into a space right between recreational and serious math. I use a recurrence but not a generating function. Recreational math just wants to know the answer for 100, so a program suffices (or some clever by-hand recurrences, which are also in my paper). Serious math people are happy to show that a formula CAN be derived and to refine that in terms of how quickly the coefficients can be found.
- There is a gap between recreational and serious math. In particular- the serious people aren't talking to (or posting on websites to) the rec people.
- Different terminologies. I was looking for ``change problems'' and ``coin problems'' and things like that when I should have been looking for ``Sylvester Denumerant'' or ''Frobenius problem''