Nafi' (may Allah have mercy on him) said that whenever Sayyiduna Abdullah bin Umar (may Allah be pleased with him) arrived for Hajj or Umrah, he would walk briskly for three rounds and slowly for four, and he would say that the Prophet (peace and blessings be upon him) used to do the same.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9271