I've heard in a movie that for any sequence of numbers, there is a nice formula for generating that sequence. So, for example if I write:
There is a formula for generating it, though it is not an obvious one (to me). Where as
is simply the fibonacci sequence with a(n) = a(n-1) + a(n-2). If the above is true, could you point me to some papers about it? I understand elementary number theory and some abstract algebra.
Thanks. I want to apply this to patterns in music.
EDIT: (How are you supposed to reply?)
Yes, finite sequences. What I mean is for any sequence that can be given, that asks for a formula, it's usually given in finite form, with ellipses indicating that it can be continued or that there is a pattern. And in music, you're usually dealing with finite songs. So yes, finite. Sorry for my lack of mathematical rigor, I've been out of the math mode for a few months. I'll pick up the ball soon enough! :D
So, again, a formula that accounts for the finite sequence given (at least), or one that could also give the rest of the sequence (which could be anything really) - it really doesn't matter for my uses.
Thanks for the quick responses. These stack exchanges are truly the best resources for info exchange, help, and community.