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A270925
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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.
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0
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1, 1, 1, 1, 2, 2, 4, 6, 10, 16, 26, 43, 69, 112, 181, 294, 475, 768, 1243, 2012, 3255, 5267, 8523, 13790, 22313, 36103, 58416, 94519, 152934, 247453, 400387, 647841, 1048228, 1696069, 2744297, 4440365, 7184662, 11625027, 18809689, 30434716, 49244405, 79679122, 128923527, 208602649, 337526177
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OFFSET
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0,5
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COMMENTS
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F(n) is the Fibonacci(n) for integer n.
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.
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LINKS
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PROG
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(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);
a(n) = round(abs(f(n)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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