11.6

Part of 1995 All-Russian Olympiad Regional Round

Problems(1)

Source:

a_n

satisfies a_{m\plus{}n}\plus{} a_{m\minus{}n}\equal{}\frac12(a_{2m}\plus{}a_{2n}) for all

m\geq n\geq 0

. If a_1\equal{}1, find

a_{1995}

inductionalgebra proposedalgebra