[NickPollard]

There are essentially two bits of information in the 'state' of this iterated algorithm: a) Are all the non-lowest bits zero, or are they the value of the latest N b) the value of the lowest bit

So the cycle of (N, 1, N+3, 0) corresponds to (A) and (B) being: (0,0), (0,1), (1,1), (1, 0) - i.e. the 4 possible combinations of these states.