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a_{n+1} = [\sqrt[3]{a_n +n}]^3

Source: Austrian - Polish 1993 APMC

May 3, 2020
floor functionrecurrence relationSequencealgebra

Problem Statement

The sequence (an)(a_n) is defined by a0=0a_0 = 0 and an+1=[an+n3]3a_{n+1} = [\sqrt[3]{a_n +n}]^3 for n≥0n \ge 0. (a) Find ana_n in terms of nn. (b) Find all nn for which an=na_n = n.
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