A293642 a(n) is the greatest integer k such that k/Fibonacci(n) < 3/5.

0, 0, 0, 1, 1, 3, 4, 7, 12, 20, 33, 53, 86, 139, 226, 366, 592, 958, 1550, 2508, 4059, 6567, 10626, 17194, 27820, 45015, 72835, 117850, 190686, 308537, 499224, 807761, 1306985, 2114746, 3421732, 5536479, 8958211, 14494690, 23452901, 37947591, 61400493

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, 2, 1, -3, -1, 3, 0, -2, 1, 2, -1, -1)

Formula

G.f.: (x^3 (1 + x^4) (1 - x^4 + x^6))/((-1 + x) (-1 + x + x^2) (1 + x + x^2 + x^3 + x^4) (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) + 2 a(n-5) + a(n-6) - 3 a(n-7) - a(n-8) + 3 a(n-9) - 2 a(n-11) + a(n-12) + 2 a(n-13) - a(n-14) - a(n-15) for n >= 16.

a(n) = floor(3*Fibonacci(n)/5).

a(n) = A293643(n) - 1 for n > 0.

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 *)

Crossrefs

Cf. A000045, A293643, A293644.

Sequence in context: A117950 A025047 A050342 * A214286 A340359 A108700

Adjacent sequences: A293639 A293640 A293641 * A293643 A293644 A293645

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2017

Status

approved