Heh I dont know how feasible this is in the lab.. but on paper it looks good!
Bayer-villiger reaction on cyclopentanone to obtain lactone.
Cleavage of lactone to produce the 5-hydroxy-pentanoic acid
Oxidize to make an aldehyde out of the alcohol.
Aldol reaction to produce the 1-butenoic acid.
make a ketone outta the double bond and remove the carboxylic acid by de-carboxylating it.
From there it should be pretty straight forward, I dont think the last few steps of my synthesis would work at all in the lab... just paper dreams