That should actually be:
route add -net 10.0.0.0 netmask 255.255.240.0 gw 10.0.0.1
that should tell the router "ok, everything in the range 10.0.0.0/20 (10.0.0.1 up to 10.0.15.254) should be send to 10.0.0.1"
If you have your network settings correctly setup on your router, this route should already be there.
see: route -n