T.A.J. Express: Train from A to JDiscrete Mathematics Level pending
A is the originating railway station and J is the terminating station, with eight way stations B, C, D, E, F, G, H, and I, en route. Train is scheduled to halt at some way stations and run through some. In how many ways the train can move from A to J in such a way that it neither halts at three consecutive stations nor runs through three consecutive stations?
Note: Both B and C (or H and I) cannot be halts as train starts and ends at A and J, respectively.