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Let {a (n)} ( n -1) ^(oo) be a sequene ...

Let `{a _(n)} _( n -1) ^(oo) ` be a sequene such that `a _(1) = 1, a _(2) = 1 and a _( n+2) = 2 a _( n +1) + a _(n)` for all ` n ge 1.` Then the value of `47 sum _( n -1) ^(oo) ( a _(n))/( 2 ^( 3n))` is equal to ____________.

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