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A270925 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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..44.

PROG

(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)));

CROSSREFS

Cf. A000045.

Sequence in context: A055389 A163733 A198834 * A084202 A300865 A053637

Adjacent sequences:  A270922 A270923 A270924 * A270926 A270927 A270928

KEYWORD

nonn

AUTHOR

Altug Alkan, Apr 05 2016

STATUS

approved

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Last modified June 18 06:55 EDT 2019. Contains 324203 sequences. (Running on oeis4.)