%N Nearest integer to absolute value of the function f(n) where f(n) is the derivative of F(n) = ((1/2+sqrt(5)/2)^n-(1/2-sqrt(5)/2)^n)/sqrt(5) with respect to n.
%C F(n) is the Fibonacci(n) for integer n.
%C Since F(n) is the sum of F(n-1) and F(n-2), the derivative of F(n) is simply the sum of the derivatives of F(n-1) and F(n-2). So sum of the two consecutive terms is generally equal to next term of this sequence.
%o (PARI) f(n) = -((sqrt(5)-1)^n*(log(-1)-log(2)+log(sqrt(5)-1))*(-1)^n+(1+sqrt(5))^n*(log(2)-log(sqrt(5)+1)))/(sqrt(5)*2^n);
%o a(n) = round(abs(f(n)));
%Y Cf. A000045.
%A _Altug Alkan_, Apr 05 2016