Does "one seat over" mean someone is in the middle between this couple?

"So I walked over to the Astor on Broadway.
And would you believe it?
Who walks in and sits one seat over,
but the girl in the carnation-pink coat."

Question

Does "one seat over" mean someone is in the middle between this couple?

"So I walked over to the Astor on Broadway.
And would you believe it?
Who walks in and sits one seat over,
but the girl in the carnation-pink coat."

Answer

It means that there was one seat between the speaker and the girl.

Another way to say this would be: "She was sitting in the next seat but one."

Answer

I think it means next to