%I
%S 1,1,1,1,2,2,4,6,10,16,26,43,69,112,181,294,475,768,1243,2012,3255,
%T 5267,8523,13790,22313,36103,58416,94519,152934,247453,400387,647841,
%U 1048228,1696069,2744297,4440365,7184662,11625027,18809689,30434716,49244405,79679122,128923527,208602649,337526177
%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(1/2sqrt(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(n1) and F(n2), the derivative of F(n) is simply the sum of the derivatives of F(n1) and F(n2). 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.
%K nonn
%O 0,5
%A _Altug Alkan_, Apr 05 2016
