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%I #7 Feb 17 2018 20:06:11
%S 0,1,1,2,2,3,5,8,13,21,33,54,87,140,227,366,593,959,1551,2509,4059,
%T 6568,10627,17195,27821,45015,72836,117851,190687,308538,499224,
%U 807762,1306986,2114747,3421733,5536479,8958212,14494691,23452902,37947592,61400493
%N a(n) is the least integer k such that k/Fibonacci(n) > 3/5.
%H Clark Kimberling, <a href="/A293643/b293643.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -1, -2, 2, 1, -3, -1, 3, 0, -2, 1, 2, -1, -1)
%F G.f.: -((x (-1 + x^2 + x^3 - x^8 + x^12 + x^13))/((-1 + x) (-1 + x +
%F x^2) (1 + x + x^2 + x^3 + x^4) (1 - x^2 + x^4 - x^6 + x^8))).
%F a(n) = a(n-1) + 2 a(n-2) - a(n-3) - 2 a(n-4) + 2 a(n-5) + a(n-6) - 3 a(n-7) - a(n-8) + 3 a(n-9) - 2 a(n-11) + a(n-12) + 2 a(n-13) - a(n-14) - a(n-15) for n >= 16.
%F a(n) = ceiling(3*Fibonacci(n)/5).
%F a(n) = A293642(n) + 1 for n > 0.
%t z = 120; r = 3/5; f[n_] := Fibonacci[n];
%t Table[Floor[r*f[n]], {n, 0, z}]; (* A293642 *)
%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293643 *)
%t Table[Round[r*f[n]], {n, 0, z}]; (* A293644 *)
%Y Cf. A000045, A293642, A293644.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Oct 14 2017
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