A234368 Floor(AGM(1, Fibonacci(n))), where AGM denotes the arithmetic-geometric mean.

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

Author

Alex Ratushnyak, Dec 25 2013

Keywords

• nonn

Examples

			a(9) = floor(AGM(1, Fibonacci(9))) = floor(AGM(1, 34)) = 10.
		

Crossrefs

Cf. A000040, A127758.

Programs

Mathematica

Table[Floor[ArithmeticGeometricMean[1, Fibonacci[n]]], {n, 1, 50}] (* Vaclav Kotesovec, May 09 2016 *)

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