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Russian 1995!

Source:

January 14, 2008
inductionalgebra proposedalgebra

Problem Statement

The sequence an a_n satisfies a_{m\plus{}n}\plus{} a_{m\minus{}n}\equal{}\frac12(a_{2m}\plus{}a_{2n}) for all m≥n≥0 m\geq n\geq 0. If a_1\equal{}1, find a1995 a_{1995}.
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