pen vs write down

pen

verb
  • To write (an article, a book, etc.). 

  • To enclose in a pen. 

noun
  • Penitentiary, i.e. a state or federal prison for convicted felons. 

  • The internal cartilage skeleton of a squid, shaped like a pen. 

  • An enclosure (enclosed area) used to contain domesticated animals, especially sheep or cattle. 

  • A female swan. 

  • Penalty. 

  • A writer, or their style. 

  • The bullpen. 

  • Marks of ink left by a pen. 

  • A light pen. 

  • A wing. 

  • A tool, originally made from a feather but now usually a small tubular instrument, containing ink used to write or make marks. 

write down

verb
  • To write (something) in a simple or condescending style. 

  • Used other than figuratively or idiomatically: see write, down. 

  • To produce or set (something) down in writing; to record something. 

  • To make a downward adjustment in the value of an asset. 

  • To condemn in writing; to document the faults, offenses, or wrongdoing of. 

How often have the words pen and write down occurred in a corpus of books? (source: Google Ngram Viewer )