A293643 a(n) is the least integer k such that k/Fibonacci(n) > 3/5.

0, 1, 1, 2, 2, 3, 5, 8, 13, 21, 33, 54, 87, 140, 227, 366, 593, 959, 1551, 2509, 4059, 6568, 10627, 17195, 27821, 45015, 72836, 117851, 190687, 308538, 499224, 807762, 1306986, 2114747, 3421733, 5536479, 8958212, 14494691, 23452902, 37947592, 61400493

Offset

0,4

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 (-1 + x^2 + x^3 - x^8 + x^12 + x^13))/((-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) = ceiling(3*Fibonacci(n)/5).

a(n) = A293642(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, A293642, A293644.

Sequence in context: A243853 A293419 A277218 * A022863 A236393 A350504

Adjacent sequences: A293640 A293641 A293642 * A293644 A293645 A293646

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2017

Status

approved