Odd Sequence

A Sequence of $n$ 0s and 1s is called an odd sequence if each of the $n$ Sums $\sum_{i=1}^{n-k} a_i a_{i+k}$ for $k=0$, 1, ..., $n-1$ is odd.

References

Guy, R. K. ``Odd Sequences.'' §E38 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 238-239, 1994.