Check if string matches pattern

How do I check if a string matches the following pattern?

Uppercase letter, number(s), uppercase letter, number(s)...

Example:

• These would match:

  A1B2
  B10L1
  C1N200J1
  

• These wouldn't ('^' points to problem)

  a1B2
  ^
  A10B
     ^
  AB400
  ^
  

import re
pattern = re.compile("^([A-Z][0-9]+)+$")
pattern.match(string)