Not sure how into math you are but linear regression can be used to generate the rest of your sequence if you provide a few points.

Despite the name, linear regression can be used for any number of exponents or terms. Seasonal regression is pretty interesting too.

I learned it as part of a 300 level data analysis course through my college. Probably a bit mathier than what you're looking for.

It was a lot of linear algebra to derive the forumula but it's pretty simple in practice, pretty much just a 1 liner in R (the programming language) to do pretty interesting stuff.

All of the linear regression calculators online are pretty awful though.

I have it on my project ideas list to make a slick linear regression calculator somewhat geared towards incremental game creators. Probably won't have time to work on that for a few years unfortunately.