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perfect squares sequence, a_{n+2} +a_{n-1} = 2(a_{n+1} +a_n)

Source: Germany Federal - Bundeswettbewerb Mathematik 1990, round 1, p2

February 21, 2020
SequencePerfect Squarerecurrence relationalgebra

Problem Statement

The sequence a0,a1,a2,...a_0,a_1,a_2,... is defined by a0=0,a1=a2=1a_0 = 0, a_1 = a_2 = 1 and an+2+an−1=2(an+1+an)a_{n+2} +a_{n-1} = 2(a_{n+1} +a_n) for all n∈Nn \in N. Show that all ana_n are perfect squares .
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