Let {a0,a1,a2…,an} be the set of integers that satisfy
k=0∑n(kn)ak=Fn∀n∈{1,2,3,4,…},
where Fn is the nthFibonacci number(F1=1,F2=1,F3=2,…,Fn+1=Fn+Fn−1). Then we have n→∞limanan+1=ca+b, where a, b, and c are integers with a>0 and b square-free. What is a+b+c?
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