Enjoy Comfortable, Affordable Downtown Baton Rouge City Life. The 440 on Third offers 65 modern, LEED-certified apartments with amenities you might expect to find far outside Baton Rouge?s business and entertainment district. It?s the perfect place to make your home in the midst of downtown?s bustling core. Many amenities await you including a grocery store on the bottom floor. Everything you need is at 440 on Third.