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A293638 a(n) is the integer k that minimizes |k/Fibonacci(n) - 1/5|. 2
0, 0, 0, 0, 1, 1, 2, 3, 4, 7, 11, 18, 29, 47, 75, 122, 197, 319, 517, 836, 1353, 2189, 3542, 5731, 9274, 15005, 24279, 39284, 63562, 102846, 166408, 269254, 435662, 704916, 1140577, 1845493, 2986070, 4831563, 7817634, 12649197, 20466831, 33116028, 53582859 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

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.: ((-1 + x) x^4 (1 + x))/((-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 + F(n)/5).

a(n) = A004698(n) if (fractional part of Fibonacci(n)/5) < 1/2, otherwise a(n) = A293637(n).

MATHEMATICA

z = 120; r = 1/5; f[n_] := Fibonacci[n];

Table[Floor[r*f[n]], {n, 0, z}];   (* A004698 *)

Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293637 *)

Table[Round[r*f[n]], {n, 0, z}];   (* A293638 *)

CROSSREFS

Cf. A000045, A004698, A293637.

Sequence in context: A222329 A018145 A050195 * A222330 A222331 A222332

Adjacent sequences:  A293635 A293636 A293637 * A293639 A293640 A293641

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 14 2017

STATUS

approved

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Last modified June 24 02:02 EDT 2021. Contains 345405 sequences. (Running on oeis4.)