A293552 a(n) is the least integer k such that k/Fibonacci(n) > 1/4.

0, 1, 1, 1, 1, 2, 2, 4, 6, 9, 14, 23, 36, 59, 95, 153, 247, 400, 646, 1046, 1692, 2737, 4428, 7165, 11592, 18757, 30349, 49105, 79453, 128558, 208010, 336568, 544578, 881145, 1425722, 2306867, 3732588, 6039455, 9772043, 15811497, 25583539, 41395036, 66978574

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, 1, -1, -1)

Formula

G.f.: -((x (-1 + x^2 + x^3 + x^5 + x^6))/((-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) = ceiling(Fibonacci(n)/4).

a(n) = A004697(n) + 1 for n > 0.

Mathematica

z = 120; r = 1/4; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A004697 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293552 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293553 *)

Crossrefs

Cf. A000045, A293552, A293553.

Sequence in context: A018139 A293640 A025049 * A293546 A366910 A052012

Adjacent sequences: A293549 A293550 A293551 * A293553 A293554 A293555

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2017

Status

approved