A293546 - OEIS

%I #7 Feb 17 2018 20:05:07

%S 0,1,1,2,2,4,6,9,14,23,37,60,96,156,252,407,658,1065,1723,2788,4510,

%T 7298,11808,19105,30912,50017,80929,130946,211874,342820,554694,

%U 897513,1452206,2349719,3801925,6151644,9953568,16105212,26058780,42163991,68222770

%N a(n) is the least integer k such that k/Fibonacci(n) > 2/3.

%H Clark Kimberling, <a href="/A293546/b293546.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, 1, 0, 0, 0, 0, 0, 1, -1, -1)

%F G.f.: (x^3 (1 + x + x^2) (1 - x^2 + x^3))/((-1 + x) (1 + x) (1 + x^2) (-1 + x + x^2) (1 + x^4)).

%F a(n) = a(n-1) + a(n-2) + a(n-8) - a(n-9) - a(n-10) for n >= 11.

%F a(n) = ceiling(2*Fibonacci(n)/3).

%F a(n) = A293545(n) + 1 for n > 0.

%t z = 120; r = 2/3; f[n_] := Fibonacci[n];

%t Table[Floor[r*f[n]], {n, 0, z}];   (* A293545 *)

%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293546 *)

%t Table[Round[r*f[n]], {n, 0, z}];   (* A293547 *)

%Y Cf. A000045, A293545, A293547.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Oct 12 2017