A293544 a(n) is the integer k that minimizes | k/Fibonacci(n) - 1/3 |.

0, 0, 0, 1, 1, 2, 3, 4, 7, 11, 18, 30, 48, 78, 126, 203, 329, 532, 861, 1394, 2255, 3649, 5904, 9552, 15456, 25008, 40464, 65473, 105937, 171410, 277347, 448756, 726103, 1174859, 1900962, 3075822, 4976784, 8052606, 13029390, 21081995, 34111385, 55193380

Offset

0,6

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^2/((-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(Fibonacci(n)/3).

a(n) = A004696(n) + 1 for n > 0.

Mathematica

z = 120; r = 1/3; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A004696 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293543 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293544 *)

Crossrefs

Cf. A000045, A004696, A293544.

Sequence in context: A080023 A169985 A254729 * A080074 A317767 A018064

Adjacent sequences: A293541 A293542 A293543 * A293545 A293546 A293547

Keyword

nonn,easy

Author

Clark Kimberling, Oct 12 2017

Status

approved