A293641 a(n) is the integer k that minimizes |k/Fibonacci(n) - 2/5|.

0, 0, 0, 1, 1, 2, 3, 5, 8, 14, 22, 36, 58, 93, 151, 244, 395, 639, 1034, 1672, 2706, 4378, 7084, 11463, 18547, 30010, 48557, 78567, 127124, 205692, 332816, 538508, 871324, 1409831, 2281155, 3690986, 5972141, 9663127, 15635268, 25298394, 40933662, 66232056

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, 2, -1, -2, 1, 2, -1, -2, 1, 1)

Formula

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

a(n) = A293639(n) if (fractional part of 2*F(n)/5) < 1/2, otherwise a(n) = A293640(n).

Mathematica

z = 120; r = 2/5; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A293639 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293640 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293641 *)

Crossrefs

Cf. A000045, A293639, A293640.

Sequence in context: A212607 A056366 A000046 * A293553 A131132 A293545

Adjacent sequences: A293638 A293639 A293640 * A293642 A293643 A293644

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2017

Status

approved