Start with one 1 in the infinite vector of zeros, shift one right or left and sum mod 2 (bitwise-XOR) to get 11, then shift two steps and XOR to get 1111, then three steps and XOR to get 1110111, then four steps and so on.

A068053

Start with one 1 in the infinite vector of zeros, shift one right or left and sum mod 2 (bitwise-XOR) to get 11, then shift two steps and XOR to get 1111, then three steps and XOR to get 1110111, then four steps and so on.