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A293552 a(n) is the least integer k such that k/Fibonacci(n) > 1/4.

%I A293552 #8 Feb 17 2018 20:05:19
%S A293552 0,1,1,1,1,2,2,4,6,9,14,23,36,59,95,153,247,400,646,1046,1692,2737,
%T A293552 4428,7165,11592,18757,30349,49105,79453,128558,208010,336568,544578,
%U A293552 881145,1425722,2306867,3732588,6039455,9772043,15811497,25583539,41395036,66978574
%N A293552 a(n) is the least integer k such that k/Fibonacci(n) > 1/4.
%H A293552 Clark Kimberling, <a href="/A293552/b293552.txt">Table of n, a(n) for n = 0..1000</a>
%H A293552 <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 A293552 G.f.: -((x (-1 + x^2 + x^3 + x^5 + x^6))/((-1 + x) (1 + x) (1 - x + x^2) (-1 + x + x^2) (1 + x + x^2))).
%F A293552 a(n) = a(n-1) + a(n-2) + a(n-6) - a(n-7) - a(n-8) for n >= 9.
%F A293552 a(n) = ceiling(Fibonacci(n)/4).
%F A293552 a(n) = A004697(n) + 1 for n > 0.
%t A293552 z = 120; r = 1/4; f[n_] := Fibonacci[n];
%t A293552 Table[Floor[r*f[n]], {n, 0, z}];   (* A004697 *)
%t A293552 Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293552 *)
%t A293552 Table[Round[r*f[n]], {n, 0, z}];   (* A293553 *)
%Y A293552 Cf. A000045, A293552, A293553.
%K A293552 nonn,easy
%O A293552 0,6
%A A293552 _Clark Kimberling_, Oct 14 2017