A293638 - OEIS

%I #7 Feb 17 2018 20:05:35

%S 0,0,0,0,1,1,2,3,4,7,11,18,29,47,75,122,197,319,517,836,1353,2189,

%T 3542,5731,9274,15005,24279,39284,63562,102846,166408,269254,435662,

%U 704916,1140577,1845493,2986070,4831563,7817634,12649197,20466831,33116028,53582859

%N a(n) is the integer k that minimizes |k/Fibonacci(n) - 1/5|.

%H Clark Kimberling, <a href="/A293638/b293638.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -1, -2, 1, 2, -1, -2, 1, 1)

%F G.f.: ((-1 + x) x^4 (1 + x))/((-1 + x + x^2) (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) + a(n-5) + 2 a(n-6) - a(n-7) - 2 a(n-8) + a(n-9) + a(n-10) for n >= 11.

%F a(n) = floor(1/2 + F(n)/5).

%F a(n) = A004698(n) if (fractional part of Fibonacci(n)/5) < 1/2, otherwise a(n) = A293637(n).

%t z = 120; r = 1/5; f[n_] := Fibonacci[n];

%t Table[Floor[r*f[n]], {n, 0, z}];   (* A004698 *)

%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293637 *)

%t Table[Round[r*f[n]], {n, 0, z}];   (* A293638 *)

%Y Cf. A000045, A004698, A293637.

%K nonn,easy

%O 0,7

%A _Clark Kimberling_, Oct 14 2017