Can you toss a coin without it flipping at least once (changing state)? I find it quite unlikely to happen, so if the starting state was H, your sequence will be THTH...
I can't quite define what counts as start of sequence. Maybe a sequence should always have at least one element, and toss straight up is allowed. But if some flipping is mandatory, then the start of sequence would mean the other side of the coin. All I could deduce before this paper is the probabilty of coin flip is skewed.