A293642 - OEIS

%I #8 Feb 17 2018 20:06:05

%S 0,0,0,1,1,3,4,7,12,20,33,53,86,139,226,366,592,958,1550,2508,4059,

%T 6567,10626,17194,27820,45015,72835,117850,190686,308537,499224,

%U 807761,1306985,2114746,3421732,5536479,8958211,14494690,23452901,37947591,61400493

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

%H Clark Kimberling, <a href="/A293642/b293642.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -1, -2, 2, 1, -3, -1, 3, 0, -2, 1, 2, -1, -1)

%F 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)).

%F 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.

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

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

%t z = 120; r = 3/5; f[n_] := Fibonacci[n];

%t Table[Floor[r*f[n]], {n, 0, z}];   (* A293642 *)

%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293643 *)

%t Table[Round[r*f[n]], {n, 0, z}];   (* A293644 *)

%Y Cf. A000045, A293643, A293644.

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Oct 14 2017