MathDB
recurrences

Source: nigerian mathematics olympiad round 3 problem 2

February 21, 2020
algebra

Problem Statement

a sequence (an)(a_n) nn ≥1\geq 1 is defined by the following equations; a1=1a_1=1, a2=2a_2=2 ,a3=1a_3=1, a2n−1a_{2n-1}a2na_{2n}=a2a_2a2n−3a_{2n-3}+(a2a2n−3+a4a2n−5.....+a2n−2a1)(a_2a_{2n-3}+a_4a_{2n-5}.....+a_{2n-2}a_1) for nn ≥2\geq 2 na2nna_{2n}a2n+1a_{2n+1}=a2a_2a2n−2a_{2n-2}+(a2a2n−2+a4a2n−4.....+a2n−2a2)(a_2a_{2n-2}+a_4a_{2n-4}.....+a_{2n-2}a_2) for nn ≥2\geq 2 find a2020a_{2020}
Back to ProblemsView on AoPS