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.

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

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 * A331964 A084202 A300865

Adjacent sequences: A270922 A270923 A270924 * A270926 A270927 A270928

Keyword

nonn

Author

Altug Alkan, Apr 05 2016

Status

approved