A293547 a(n) is the integer k that minimizes |k/Fibonacci(n) - 2/3|.

0, 1, 1, 1, 2, 3, 5, 9, 14, 23, 37, 59, 96, 155, 251, 407, 658, 1065, 1723, 2787, 4510, 7297, 11807, 19105, 30912, 50017, 80929, 130945, 211874, 342819, 554693, 897513, 1452206, 2349719, 3801925, 6151643, 9953568, 16105211, 26058779, 42163991, 68222770

Offset

0,5

Links

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

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

Formula

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

a(n) = a(n-1) + a(n-2) - a(n-4) + a(n-5) + a(n-6) for n >= 7.

a(n) = floor(1/2 + 2*Fibonacci(n)/3).

a(n) = A293545(n) if (fractional part of 2*Fibonacci(n)/3) < 1/2, otherwise a(n) = A293546(n).

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, A293546.

Sequence in context: A326332 A079962 A244986 * A124502 A251572 A173714

Adjacent sequences: A293544 A293545 A293546 * A293548 A293549 A293550

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2017

Status

approved