The Big Bang Theory Season 4 Episode 16
The Cohabitation Formulation
Bernadette suggests Howard move in with her, but he's reluctant to do anything while his Ma is still alive.
Fed up with arguing with his Ma, he goes to Leonard's place to crash. Howard tries to compromise and offer to stay at Bernadette's while his Ma is out of town for a couple of days, but she gives him an ultimatum: her or his Ma. He decides on Bernadette, but expects her to do all the same things his Ma did like cooking, shopping and doing his laundry.
Unhappy with this turn of events, Bernadette stands up to Howard and says she will not be his mother, causing Howard to move back home.
After learning from Howard that Raj's sister Priya is in town and Leonard rushes over to Raj's place to see her, against Raj's wishes. After spending the night together, they decide to start dating officially, yet Raj tries to find reasons they should break up.
Meanwhile, Amy goes to Penny's place to attempt to comfort her in the wake of Priya's man stealing of Leonard. Seeing how well Priya and Leonard seem to fit for each other causes Penny to break down, while Amy attempts to use the situation for her research.