Can the following be called a recursive formula for the Fibonacci sequence 0 -> 1, 1-> 0&1 ? It means replace each 0 with 1, then replace each 1 with 0 and 1. So we get 0,1,01,101,011,10101,01101101, and so on. Sum the 0s and 1s at each stage and we get 0,1,1, 2,3,5,... Also if you swap round the constituent formulae so they go 0 -> 0&1, 1 -> 1, then we get the natural number sequence. Where can I find out more about this form of notation?
