A293673 a(n) is the integer k that minimizes |k/Fibonacci(n) - 4/5|.

0, 1, 1, 2, 2, 4, 6, 10, 17, 27, 44, 71, 115, 186, 302, 488, 790, 1278, 2067, 3345, 5412, 8757, 14169, 22926, 37094, 60020, 97114, 157134, 254249, 411383, 665632, 1077015, 1742647, 2819662, 4562310, 7381972, 11944282, 19326254, 31270535, 50596789, 81867324

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (1, 2, -1, -2, 1, 2, -1, -2, 1, 1)

Formula

G.f.: -((x (1 - x^2 - x^3 + x^4 + x^5 - x^6 + x^8))/((-1 + x + x^2) (1 - x^2 + x^4 - x^6 + x^8))).

a(n) = a(n-1) + 2 a(n-2) - a(n-3) - 2 a(n-4) + a(n-5) + 2 a(n-6) - a(n-7) - 2 a(n-8) + a(n-9) + a(n-10) for n >= 11.

a(n) = floor(1/2 + 4*Fibonacci(n)/5).

a(n) = A293671(n) if (fractional part of 4*Fibonacci(n)/5) < 1/2, otherwise a(n) = A293672(n).

Mathematica

z = 120; r = 4/5; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A293671 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293672 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293673 *)

Crossrefs

Cf. A000045, A293671, A293672.

Sequence in context: A000016 A361223 A060553 * A344707 A293505 A032307

Adjacent sequences: A293670 A293671 A293672 * A293674 A293675 A293676

Keyword

nonn,easy

Author

Clark Kimberling, Oct 16 2017

Status

approved