0 -> 1 01 -> 10 0110 -> 1001 01101001 -> 10010110 Recursively append the inverse.

This sequence is known as the Morse-Thue sequence. It can be defined non-recursively as the nth term is the mod 2 count of 1s in n written

- in binary
0->0 1->1 10->1 11->0 100->1 101->0 110->0 111->1 etc.

- Reference
- Dekking, et. al., "Folds! I,II,III" The Mathematical Intelligencer, v4,#3,#4,#4.