The ''border number'' of an $n \times n$ square is defined as the number of unit squares whose edges border the edges of the larger square. The border numbers of $1 \times 1$, $2 \times 2$, $3 \times 3$, $4 \times 4$, and $5\times 5$ squares are illustrated. What is the border number of a 20 unit by 20 unit square? [asy] pair A,B; unitsize(.25cm); for(int i = 1; i < 6; ++i){ A = ((i-1)*(i+4),0); B = (-i,-i); fill(A+B--A+B+(2*i,0)--A+B+(2*i,2*i)--A+B+(0,2*i)--cycle,grey); for(int k = 0; k < i+1; ++k){ draw(A+B+(0,2*k)--A+B+(2*i,2*k),black); draw(A+B+(2*k,0)--A+B+(2*k,2*i),black); } fill((A+B+(2,2))--A+B+((2*(i-1),2))--(A+B+(2*i-2,2*i-2))--(A+B+(2,2*i-2))--cycle,white); draw((A+B+(2,2))--A+B+((2*(i-1),2))--(A+B+(2*i-2,2*i-2))--(A+B+(2,2*i-2))--cycle,black); } fill((-1,-1)--(1,-1)--(1,1)--(-1,1)--cycle,grey); label("1",(0,-5),S); label("4",(6,-5),S); label("8",(14,-5),S); label("12",(24,-5),S); label("16",(36,-5),S); [/asy]