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A293505

a(n) is the integer k that minimizes |k/Fibonacci(n) - 1/2|.

0, 0, 0, 1, 2, 2, 4, 6, 10, 17, 28, 44, 72, 116, 188, 305, 494, 798, 1292, 2090, 3382, 5473, 8856, 14328, 23184, 37512, 60696, 98209, 158906, 257114, 416020, 673134, 1089154, 1762289, 2851444, 4613732, 7465176, 12078908, 19544084, 31622993, 51167078

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

FORMULA

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

a(n) = a(n-1) + a(n-2) + a(n-6) - a(n-7) - a(n-8) for n >= 9.

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

a(n) = A004695(n) if (fractional part of Fibonacci(n)/2) < 1/2, otherwise a(n) = A293419(n).

MATHEMATICA

z = 120; r = 1/2; f[n_] := Fibonacci[n];

Table[Floor[r*f[n]], {n, 0, z}]; (* A004695 *)

Table[Ceiling[r*f[n]], {n, 0, z}]; (* A173173 *)

Table[Round[r*f[n]], {n, 0, z}]; (* A293505 *)

CROSSREFS

Cf. A000045, A004695, A293505.

Sequence in context: A060553 A293673 A344707 * A032307 A007560 A032237

Adjacent sequences: A293502 A293503 A293504 * A293506 A293507 A293508

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 12 2017

STATUS

approved

URL: https://oeis.org/A293505

⇱ A293505 - OEIS