A293644 a(n) is the integer k that minimizes |k/Fibonacci(n) - 3/5|.

0, 1, 1, 1, 2, 3, 5, 8, 13, 20, 33, 53, 86, 140, 226, 366, 592, 958, 1550, 2509, 4059, 6568, 10627, 17194, 27821, 45015, 72836, 117851, 190687, 308537, 499224, 807761, 1306985, 2114747, 3421732, 5536479, 8958211, 14494690, 23452901, 37947592, 61400493

Offset

0,5

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)^2 x (1 + x)^2 (1 + 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 + 3*Fibonacci(n)/5).

a(n) = A293642(n) if (fractional part of 3*Fibonacci(n)/5) < 1/2, otherwise a(n) = A293643(n).

Mathematica

z = 120; r = 3/5; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A293642 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293643 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293644 *)
LinearRecurrence[{1, 2, -1, -2, 1, 2, -1, -2, 1, 1}, {0, 1, 1, 1, 2, 3, 5, 8, 13, 20}, 50] (* Harvey P. Dale, Oct 20 2024 *)

Crossrefs

Cf. A000045, A293642, A293643.

Sequence in context: A013985 A092834 A080106 * A158415 A005347 A100582

Adjacent sequences: A293641 A293642 A293643 * A293645 A293646 A293647

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2017

Status

approved