Not an electrician here but I have stayed at a Motel 6.
The blue wire is usually wired to a switch somewhere for controlling a second accessory like a fan. Seeing no fan here I dont know what the blue wire would be for It maybe set up for a kindof dim setting where some bulbs turn off?
Anyway, the black wire should go to the black house wire and the red should go to the white house wire. I would leave the blue disconnected at first while checking if this scheme works. If only some bulbs light then try to connect the blue and black to the house black.