A Fibonacci Sum

A sequence {ai}i=1n\{a_i\}_{i=1}^n has the property that Sn=FnS_n=F_n where Sn=i=1naiS_n=\displaystyle\sum^n_{i=1}a_i, F1=1F_1=1, F2=1F_2=1, and Fn=Fn1+Fn2F_n=F_{n-1}+F_{n-2}. The closed form of i=1na2i1\displaystyle\sum^n_{i=1}a_{2i-1} can be represented as Sf(n)+cS_{f(n)}+c where f(n)f(n) is a function of nn and cc is a constant. Find the last three digits of f(2013)+cf(2013)+c.

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