Q16 Matemática  (IMO Shortlist 2001)

Seja $a_1=11^{11},a_2=12^{12},a_3=13^{13}$ e $a_n=|a_{n-1}-a_{n-2}|+|a_{n-2}-a_{n-3}|,n\ge 4.$ Determine $a_{14^{14}}$.