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a(n) = Fibonacci(k) where k = floor( n*(1+sqrt(5))/2 ).
3

%I #29 Jan 11 2022 15:01:47

%S 0,1,2,3,8,21,34,89,144,377,987,1597,4181,10946,17711,46368,75025,

%T 196418,514229,832040,2178309,3524578,9227465,24157817,39088169,

%U 102334155,267914296,433494437,1134903170,1836311903,4807526976,12586269025,20365011074,53316291173,139583862445,225851433717,591286729879,956722026041,2504730781961,6557470319842

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

%C Another version of A107858.

%H G. C. Greubel, <a href="/A185381/b185381.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A000045(A000201(n)). - _Michel Marcus_, Jan 11 2022

%t Table[Fibonacci[Floor[n*GoldenRatio]],{n,0,50}] (* _Harvey P. Dale_, May 24 2016 *)

%o (PARI) for(n=0,50, print1(fibonacci(floor(n*(1+sqrt(5))/2)), ", ")) \\ _G. C. Greubel_, Jun 28 2017

%o (Python)

%o from math import isqrt

%o from sympy import fibonacci

%o def A185381(n): return fibonacci((n+isqrt(5*n**2))//2) # _Chai Wah Wu_, Jan 11 2022

%Y Cf. A000045, A000201, A107858.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, May 06 2012