## Pairs of Squares

### Info

Denote the elements of the field `$F_4$`

by `$\{0, 1, w, w + 1\}$`

, where `$w$`

satisfies the following equation with coefficients in `$F_2: w^2 + w + 1 = 0$`

.
Pairs of Squares is a recurrent double sequence defined by `$a(i, 0) = a(0, j) = 1$`

and `$a(i, j) = f(a(i, j-1), a(i-1, j-1), a(i-1, j))$`

,
where `$f(x, y, z) = (w + 1) x + (w + 1) y^2 + (w + 1) z$`

.
This recurrent double sequence can be also obtained using a system of substitutions of type 4 -> 8 with 59 rules.

The system of substitutions is too large to be presented here.

### Patch