Nair has puzzle pieces shaped like an equilateral triangle. She has pieces of two sizes: large and small. Nair build triangular figures by following these rules: $\bullet$ Figure $1$ is made up of $4$ small pieces, Figure $2$ is made up of $2$ large pieces and $8$ small, Figure $3$ by $6$ large and $12$ small, and so on. $\bullet$ The central column must be made up exclusively of small parts. $\bullet$ Outside the central column, only large pieces can be placed. Following the pattern, how many pieces will Nair use to build Figure $20$?