Give a regular description for the set of words obtained by intercaling three words $w_1,w_2,w_3$ over $\{0,1\}$ with the same length and such that the sum of the natural values obtained from $w_1,w_2$ by interpreting them as a binary numbers, that is $\mathtt{value}_2(w_1)+\mathtt{value}_2(w_2)$, coincides with $\mathtt{value}_2(w_3)$. Intercaling $n$ words $w_1,\ldots,w_n$ over $\{0,1\}$ and with the same length gives as result a word whose sequence of symbols is: the first symbol of $w_1$, the first symbol of $w_2$, …, the first symbol of $w_n$, the second symbol of $w_1$, the second symbol of $w_2$, …, the second symbol of $w_n$, the third symbol of $w_1$, and so on.