A293543 a(n) is the least integer k such that k/Fibonacci(n) > 1/3.

0, 1, 1, 1, 1, 2, 3, 5, 7, 12, 19, 30, 48, 78, 126, 204, 329, 533, 862, 1394, 2255, 3649, 5904, 9553, 15456, 25009, 40465, 65473, 105937, 171410, 277347, 448757, 726103, 1174860, 1900963, 3075822, 4976784, 8052606, 13029390, 21081996, 34111385, 55193381

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, 0, 0, 0, 0, 1, -1, -1)

Formula

G.f.: -((x (-1 + x^2 + x^3 + x^7 + x^8))/((-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) = 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 *)
LinearRecurrence[{1, 1, 0, 0, 0, 0, 0, 1, -1, -1}, {0, 1, 1, 1, 1, 2, 3, 5, 7, 12}, 50] (* Harvey P. Dale, Oct 18 2018 *)

Crossrefs

Cf. A000045, A004696, A293544.

Sequence in context: A335093 A143642 A192685 * A060986 A359742 A054540

Adjacent sequences: A293540 A293541 A293542 * A293544 A293545 A293546

Keyword

nonn,easy

Author

Clark Kimberling, Oct 12 2017

Status

approved