A293546 a(n) is the least integer k such that k/Fibonacci(n) > 2/3.

0, 1, 1, 2, 2, 4, 6, 9, 14, 23, 37, 60, 96, 156, 252, 407, 658, 1065, 1723, 2788, 4510, 7298, 11808, 19105, 30912, 50017, 80929, 130946, 211874, 342820, 554694, 897513, 1452206, 2349719, 3801925, 6151644, 9953568, 16105212, 26058780, 42163991, 68222770

Offset

0,4

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, 0, 0, 0, 1, -1, -1)

Formula

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)).

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

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

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

Mathematica

z = 120; r = 2/3; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A293545 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293546 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293547 *)

Crossrefs

Cf. A000045, A293545, A293547.

Sequence in context: A293640 A025049 A293552 * A366910 A052012 A234961

Adjacent sequences: A293543 A293544 A293545 * A293547 A293548 A293549

Keyword

nonn,easy

Author

Clark Kimberling, Oct 12 2017

Status

approved