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Consider the sequence {an}\left\{a_{n}\right\}{an} where a1=0a_{1}=0a1=0 and an+1=an+1+21+ana_{n+1}=a_{n}+1+2\sqrt{1+a_{n}}an+1=an+1+21+an for natural numbers nnn.
Find the value of a2009a_{2009}a2009.
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