# Math Help - While I'm at it, here's an OGF that has a sticky wicket!

1. ## While I'm at it, here's an OGF that has a sticky wicket!

$c_{0}=2,\, c_{1}=0,\,\, c_{n}=2c_{n-1}-2c_{n-2}\,\,\, n\geq2
$

$\sum_{n\geq2}c_{n}x^{n}=\sum_{n\geq2}2c_{n-1}x^{n}-\sum_{n\geq2}2c_{n-2}x^{n}$

$f(x)-2=2x(f(x)-2)-2x^{2}f(x)$

$f(x)-2xf(x)+2x^{2}f(x)=-4x+2$

$f(x)=\frac{-4x+2}{2x^{2}-2x+1}$

$\frac{2\pm\sqrt{4-4(2)}}{4}=\frac{2\pm2i}{4}$

I'm just not sure where to go from here. Where ever that is, I've heard you can't get there from here. Any help would be greatly appreciated.

2. Is the fact that the roots of $2x^2 - 2x + 1$ are complex bothering you?

If so, just march on and use partial fractions as if the roots were real. It should all work out in the end.