Actually the PC's vault was designed to never open... maybe the Vault-Tec heads went there, as there was no real experiment (other than never ending the vault life).
Actually, according to http://fallout.wikia.com/wiki/Vault_101 Vault 101 was an experiment there, it was to:
The purpose of Vault 101 in the Vault Experiment was not only to test the results of indefinite isolation, but also had a greater purpose of testing the role of the Overseer. This Vault was sealed before the bombs ever even hit, and the residents were kept in the dark as to the true nature of the aftermath, receiving fake radio transmissions which painted a far bleaker picture than even the Wasteland offered. It was the Overseer's job to keep this secret and make sure the Vault stayed sealed, and the first Overseer was actually a trained Vault-Tec official.
One could say there are more vaults there because of the massive number of people on the east coast. Possibly the west coast was less populated in the fallout out world. FO3 actually mentions this a little bit, in random mailboxs you can get a letter that says "We're sorry you didn't get selected for your chosen vault, but you have been added to the waiting list. Please consider moving to an area where there is not waiting list for the vaults, such as Oklahoma."
Basically Vault Tek knew they had a lot of vaults, and knew they didn't have a lot. Places that are sparsely populated (which is most of the FO1 and 2 world maps) have less vaults because less people what or can afford to be in.