2001 IMO Shortlist S20

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

设 $a_1 = 11^{11}, \, a_2 = 12^{12}, \, a_3 = 13^{13}$ 和 $a_n = |a_{n - 1} - a_{n - 2}| + |a_{n - 2} - a_{n - 3}|, n \geq 4.$ 确定 $a_{14^{14}}$ 。