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%I #7 Feb 17 2018 20:05:13
%S 0,1,1,1,2,3,5,9,14,23,37,59,96,155,251,407,658,1065,1723,2787,4510,
%T 7297,11807,19105,30912,50017,80929,130945,211874,342819,554693,
%U 897513,1452206,2349719,3801925,6151643,9953568,16105211,26058779,42163991,68222770
%N a(n) is the integer k that minimizes |k/Fibonacci(n) - 2/3|.
%H Clark Kimberling, <a href="/A293547/b293547.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, -1, 1, 1)
%F G.f.: -((x (1 - x^2 + x^4))/((-1 + x + x^2) (1 + x^4))).
%F a(n) = a(n-1) + a(n-2) - a(n-4) + a(n-5) + a(n-6) for n >= 7.
%F a(n) = floor(1/2 + 2*Fibonacci(n)/3).
%F a(n) = A293545(n) if (fractional part of 2*Fibonacci(n)/3) < 1/2, otherwise a(n) = A293546(n).
%t z = 120; r = 2/3; f[n_] := Fibonacci[n];
%t Table[Floor[r*f[n]], {n, 0, z}]; (* A293545 *)
%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293546 *)
%t Table[Round[r*f[n]], {n, 0, z}]; (* A293547 *)
%Y Cf. A000045, A293545, A293546.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Oct 14 2017
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