Is Itikaf for the entire month of Ramadan contrary to the Sunnah?

The Sunnah that the Prophet (peace be upon him) consistently observed regarding I'tikaf (seclusion in the mosque) is the last ten nights of Ramadan. He also performed I'tikaf for the entire month once, and it is confirmed that he observed I'tikaf for twenty days in the year he passed away. Therefore, whoever performs I'tikaf for the entire month, or for twenty days, or for the last ten nights, has indeed followed the Sunnah.