Find formula for f(x)

[miami_shadows]

I've come across this problem and I have no idea where to begin.

Find the formula for f(x), given the following series:
 

Comments

[madcaptenor]

The idea behind saying c_{n+4} = c_n is that once you know c_0, c_1, c_2, c_3, you can get all the other c_n -- you have c_4 = c_0, c_5 = c_1, and so on. This is why all the answers only involve c_0, c_1, c_2, c_3.

[miami_shadows]

ah alright, that explains the numerator, but is there any connection between the highest degree in the numerator and that in the denominator?

[joshua_green]

ƒ(x) = c0 + c1x + c2x2 + c3x3 + c0x4 + c1x5 + c2x6 + c3x7 + c0x8 + c1x9 + c2x10 + c3x11 + ...
      = (c0 + c0x4 + c0x8 + ...) + (c1x + c1x5 + c1x9 + ...) + (c2x2 + c2x6 + c2x10 + ...) + (c3x3 + c3x7 + c3x11 + ...).

[miami_shadows]

I'm sorry, I don't quite understand what I should be seeing here...I recognize the pattern but not much more