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A293505 a(n) is the integer k that minimizes |k/Fibonacci(n) - 1/2|. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
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
Sequence in context: A060553 A293673 A344707 * A032307 A007560 A032237
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 12 2017
STATUS
approved

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Last modified April 23 07:57 EDT 2024. Contains 371905 sequences. (Running on oeis4.)