Year with Squares

Let $x$ be the figure number and $y$ be the number of squares in each figure. Since each figure increases by $4$ squares, the slope of the equation is $m = 4$ , and since Figure $1$ has $1$ square, the equation passes through the coordinate $(1, 1)$ .

Therefore, the equation of the line is $y - 1 = 4(x - 1)$ or $y = 4x - 3$ .

For Figure $2019$ , $x = 2019$ , so the number of squares is $y = 4 \cdot 2019 - 3 = \boxed{8073}$ .