%I #13 Sep 08 2022 08:46:19

%S 0,1,1,2,4,7,11,18,29,48,77,125,203,329,533,862,1395,2258,3654,5912,

%T 9567,15479,25047,40527,65574,106101,171675,277776,449452,727229,

%U 1176682,1903911,3080594,4984506,8065100,13049606,21114706,34164312,55279018,89443331

%N a(n) is the greatest integer k such that k/Fibonacci(n) < sqrt(2).

%H Clark Kimberling, <a href="/A293418/b293418.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor(Fibonacci(n)*sqrt(2)).

%F a(n) = A293419(n) - 1 for n > 0.

%t z = 120; r = Sqrt[2]; f[n_] := Fibonacci[n];

%t Table[Floor[r*f[n]], {n, 0, z}]; (* A293418 *)

%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293419 *)

%t Table[Round[r*f[n]], {n, 0, z}]; (* A293420 *)

%o (PARI) for(n=0,30, print1(floor(fibonacci(n)*sqrt(2)), ", ")) \\ _G. C. Greubel_, Feb 08 2018

%o (Magma) [Floor(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // _G. C. Greubel_, Feb 08 2018

%Y Cf. A000045, A293419, A293420.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Oct 12 2017