If , prove, by induction or otherwise, that =a_{n}x+b_{n}+c_{n}, where a_{1}=1, b_{1}=1, c_{1}=0, and a_{n}=a_{n-1}+b_{n-1}, b_{n}=a_{n-1}+b_{n-1}+c_{n-1}, c_{n}=a_{n-1}+c_{n-1}, for n=2,3,... .

I have got nowhere with this. I am trying to use induction. Is there a typing mistake in the question.