A185381 a(n) = Fibonacci(k) where k = floor( n*(1+sqrt(5))/2 ).

0, 1, 2, 3, 8, 21, 34, 89, 144, 377, 987, 1597, 4181, 10946, 17711, 46368, 75025, 196418, 514229, 832040, 2178309, 3524578, 9227465, 24157817, 39088169, 102334155, 267914296, 433494437, 1134903170, 1836311903, 4807526976, 12586269025, 20365011074, 53316291173, 139583862445, 225851433717, 591286729879, 956722026041, 2504730781961, 6557470319842

Offset: 0

Author

N. J. A. Sloane, May 06 2012

Keywords

• nonn

Comments

Another version of A107858.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000045, A000201, A107858.

Programs

Mathematica

Table[Fibonacci[Floor[n*GoldenRatio]],{n,0,50}] (* Harvey P. Dale, May 24 2016 *)

PARI

for(n=0,50, print1(fibonacci(floor(n*(1+sqrt(5))/2)), ", ")) \\ G. C. Greubel, Jun 28 2017

Python

from math import isqrt
from sympy import fibonacci
def A185381(n): return fibonacci((n+isqrt(5*n**2))//2) # Chai Wah Wu, Jan 11 2022

Formula

a(n) = A000045(A000201(n)). - Michel Marcus, Jan 11 2022