Re: closed form for generating function

From: hawkmoon269 (rson_at_new.rr.com)
Date: 02/01/05 

Date: 31 Jan 2005 16:31:02 -0800

Could you walk me through the partial fraction solution...? I've been
reading about generating functions in my spare time and am having a
hard time understanding all the ins and outs. I do know something
about partial fractions and tried to work it out, but I'm not sure if
my solution is correct. I got --

x / (1-nx)(1-x-x^2) = (2n+1) / n^2(1-nx) + (n+1)(1-sqrt(5) /
2(1-x-x^2).

That just doesn't seem right, though. And I'm still lost as how to use
that to get a closed form for the gf, i.e., a form like 3^n - 2^n or
n(n+1) / 2 etc...

h