Can we find $F(1) + F(2) + F(3) + \dots + F(100)$?

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The function \(F(k)\) is defined for positive integers by \(F(1)=1\), \(F(2)=1\), \(F(3)=-1\) and by the identities \[F(2k)=F(k), \qquad F(2k+1)=F(k)\] for \(k \ge 2\). The sum \[F(1) + F(2) + F(3) + \dots + F(100)\] equals

1. \(-15\);

2. \(28\);

3. \(64\);

4. \(81\).