### $0\text{-}1$ sequences having the same numbers of $\left(1\text{-}1\right)$-couples of given distances

Let $a$ be a $0-1$ sequence with a finite number of terms equal to 1. The distance sequence ${\delta}^{\left(a\right)}$ of $a$ is defined as a sequence of the numbers of $(1-1)$-couples of given distances. The paper investigates such pairs of $0-1$ sequences $a,b$ that a is different from $b$ and ${\delta}^{\left(a\right)}={\delta}^{\left(b\right)}$.