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A234368
Floor(AGM(1, Fibonacci(n))), where AGM denotes the arithmetic-geometric mean.
1
1, 1, 1, 1, 2, 3, 5, 7, 10, 16, 23, 35, 53, 80, 122, 187, 286, 439, 675, 1041, 1608, 2491, 3864, 6004, 9344, 14563, 22729, 35517, 55566, 87026, 136440, 214117, 336322, 528725, 831868, 1309817, 2063861, 3254227, 5134497, 8106188, 12805344, 20239959
OFFSET
1,5
FORMULA
a(n) ~ Pi * phi^n / (2 * sqrt(5) * log(phi) * n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio, log(phi) = A002390. - Vaclav Kotesovec, May 09 2016
EXAMPLE
a(9) = floor(AGM(1, Fibonacci(9))) = floor(AGM(1, 34)) = 10.
MATHEMATICA
Table[Floor[ArithmeticGeometricMean[1, Fibonacci[n]]], {n, 1, 50}] (* Vaclav Kotesovec, May 09 2016 *)
CROSSREFS
Sequence in context: A134792 A300795 A033068 * A052011 A278706 A005468
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Dec 25 2013
STATUS
approved