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A293505 a(n) is the integer k that minimizes |k/Fibonacci(n) - 1/2|.

%I A293505 #7 Feb 17 2018 20:04:40
%S A293505 0,0,0,1,2,2,4,6,10,17,28,44,72,116,188,305,494,798,1292,2090,3382,
%T A293505 5473,8856,14328,23184,37512,60696,98209,158906,257114,416020,673134,
%U A293505 1089154,1762289,2851444,4613732,7465176,12078908,19544084,31622993,51167078
%N A293505 a(n) is the integer k that minimizes |k/Fibonacci(n) - 1/2|.
%H A293505 Clark Kimberling, <a href="/A293505/b293505.txt">Table of n, a(n) for n = 0..1000</a>
%H A293505 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, 0, 1, -1, -1)
%F A293505 G.f.: -((x^3 (-1 - x + x^2))/((-1 + x) (1 + x) (1 - x + x^2) (-1 + x + x^2) (1 + x + x^2))).
%F A293505 a(n) = a(n-1) + a(n-2) + a(n-6) - a(n-7) - a(n-8) for n >= 9.
%F A293505 a(n) = floor(1/2 + Fibonacci(n)/2).
%F A293505 a(n) = A004695(n) if (fractional part of Fibonacci(n)/2) < 1/2, otherwise a(n) = A293419(n).
%t A293505 z = 120; r = 1/2; f[n_] := Fibonacci[n];
%t A293505 Table[Floor[r*f[n]], {n, 0, z}];   (* A004695 *)
%t A293505 Table[Ceiling[r*f[n]], {n, 0, z}]; (* A173173 *)
%t A293505 Table[Round[r*f[n]], {n, 0, z}];   (* A293505 *)
%Y A293505 Cf. A000045, A004695, A293505.
%K A293505 nonn,easy
%O A293505 0,5
%A A293505 _Clark Kimberling_, Oct 12 2017