A293633 a(n) is the integer k that minimizes |k/Fibonacci(n) - 3/4|.

1, 1, 2, 2, 4, 6, 10, 16, 26, 41, 67, 108, 175, 283, 458, 740, 1198, 1938, 3136, 5074, 8210, 13283, 21493, 34776, 56269, 91045, 147314, 238358, 385672, 624030, 1009702, 1633732, 2643434, 4277165, 6920599, 11197764, 18118363, 29316127, 47434490, 76750616

Offset

1,3

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,1,-1,-1).

Formula

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

a(n) = A293631(n) if (fractional part of 3*Fibonacci(n)/4) < 1/2, else a(n) = A293632(n).

Mathematica

z = 120; r = 3/4; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 1, z}];   (* A293631 *)
Table[Ceiling[r*f[n]], {n, 1, z}]; (* A293632 *)
Table[Round[r*f[n]], {n, 1, z}];   (* A293633 *)
LinearRecurrence[{1, 1, 0, 0, 0, 1, -1, -1}, {1, 1, 2, 2, 4, 6, 10, 16}, 40] (* Harvey P. Dale, Mar 30 2019 *)

Prog

(PARI) a(n) = round(3*fibonacci(n)/4); \\ Andrew Howroyd, Feb 12 2018

Crossrefs

Cf. A000045, A293631, A293632.

Sequence in context: A288006 A228807 A262258 * A006355 A055389 A163733

Adjacent sequences: A293630 A293631 A293632 * A293634 A293635 A293636

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2017

Extensions

Offset changed by Clark Kimberling, Feb 12 2018

Status

approved