I heard this while on a tour of the Denver Mint. I asked the tour guide to repeat it, because I always thought there were twelve. He said there were 12 main banks and 25 branch banks. So I went hunting. The only evidence I've found so far is a PDF-format document on the Federal Reserve web site (specifically, in the "Overview" section on the Purposes & Functions page).
An excerpt from that page:
A network of twelve Federal Reserve Banks and their twenty-five Branches carries out a variety of System functions...
A table, from a few pages farther along:
| 1 | A | Boston | |
|---|---|---|---|
| 2 | B | New York | Buffalo |
| 3 | C | Philadelphia | |
| 4 | D | Cleveland | Cincinnati Pittsburgh |
| 5 | E | Richmond | Baltimore Charlotte |
| 6 | F | Atlanta | Birmingham Jacksonville Miami Nashville New Orleans |
| 7 | G | Chicago | Detroit |
| 8 | H | St. Louis | Little Rock Louisville Memphis |
| 9 | I | Minneapolis | Helena |
| 10 | J | Kansas City | Denver Oklahoma City Omaha |
| 11 | K | Dallas | El Paso Houston San Antonio |
| 12 | L | San Francisco | Los Angeles Portland Salt Lake City Seattle |