A293641 - OEIS

%I #7 Feb 17 2018 20:05:59

%S 0,0,0,1,1,2,3,5,8,14,22,36,58,93,151,244,395,639,1034,1672,2706,4378,

%T 7084,11463,18547,30010,48557,78567,127124,205692,332816,538508,

%U 871324,1409831,2281155,3690986,5972141,9663127,15635268,25298394,40933662,66232056

%N a(n) is the integer k that minimizes |k/Fibonacci(n) - 2/5|.

%H Clark Kimberling, <a href="/A293641/b293641.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.: -((x^3 (1 - x^2 + x^4))/((-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 + 2*Fibonacci(n)/5).

%F a(n) = A293639(n) if (fractional part of 2*F(n)/5) < 1/2, otherwise a(n) = A293640(n).

%t z = 120; r = 2/5; f[n_] := Fibonacci[n];

%t Table[Floor[r*f[n]], {n, 0, z}];   (* A293639 *)

%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293640 *)

%t Table[Round[r*f[n]], {n, 0, z}];   (* A293641 *)

%Y Cf. A000045, A293639, A293640.

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Oct 14 2017